BibTex RIS Kaynak Göster

Yıl 2011, Cilt: 1 Sayı: 1, 55 - 58, 01.01.2011

Yüksel Soykan Melih Göcen

Öz

Kaynakça

  • [1]Bakhvalov, NS., Knyazev, AV., Parashkevov, R R. 2002. Extension theorems for Stokes and Lamé equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficients. Numer. Linear Algebr., 9: 115-139.
  • [2]Chizhonkov, EV. 1994. Application of the Cosserat spectrum to the optimization of a method for solving the Stokes problem. Russ. J. Numer. Anal. M., 9: 191-199.
  • [3] Chizhonkov, EV. 2009. Numerical solution to a stokes interface problem. Comp. Math., 49: 105- 116.
  • [4] Cosserat, E., Cosserat, F. 1898. Sur les èquations de la thèorie de l'èlasticitè. C. R. Acad. Sci. (Paris), 126: 1089-1091.
  • [5] Cosserat, E., Cosserat, F. 1898. Sur les fonctions potentielles de la thèorie de l'èlasticitè. C. R. Acad. Sci. (Paris), 126: 1129-1132.
  • [6] Cosserat, E., Cosserat, F. 1898. Sur la dèformation infiniment petite d'un ellipsoide èlastique. C. R. Acad. Sci. (Paris), 127: 315-318.
  • [7] Cosserat, E., Cosserat, F. 1902. Sur la solution des èquations de l'èlasticitè dans le cas où les valeurs des inconnues à la frontière sont donnèes. C. R. Acad. Sci. (Paris), 133: 145-147.
  • [8] Cosserat, E., Cosserat, F. 1902. Sur une application des fonctions potentielles de la thèorie de l'èlasticitè. C. R. Acad. Sci. (Paris), 133: 210-213
  • [9] Cosserat, E., Cosserat, F. 1902. Sur la dèformation infiniment petite d'un corps èlastique soumis à des forces donnèes. C. R. Acad. Sci. (Paris), 133: 271-273.
  • [10] Cosserat, E., Cosserat, F. 1902. Sur la dèformation infiniment petite d'une enveloppe sphèrique èlastique. C. R. Acad. Sci. (Paris), 133: 326-329.
  • [11] Cosserat, E., Cosserat, F. 1902. Sur la dèformation infiniment petite d'un ellipsoide èlastique soumis à des efforts donnèes sur la frontière. C. R. Acad. Sci. (Paris), 133: 361-364.
  • [12] Cosserat, E., Cosserat, F. 1902. Sur un point critique particulier de la solution des èquations de l'èlasticitè dans le cas où les efforts sur la frontière sont donnèes. C. R. Acad. Sci. (Paris), 133: 382-384.
  • [13] Costabel, M., Dauge. 2000. M. On the Cosserat spectrum in polygons and polyhedra, IRMAR Conference, Lausanne.
  • [14] Crouzeix, M. 1997. On an operator related to the convergenceof Uzawa's algorithm for the Stokes equation. In: M. O. Bristeau, G. Etgen, W. Fitzgibbon, J. L. Lions, J. Pèriaux and M. F. Wheeler, editors, Computational Science for the 21st Century, Wiley, Chichester, pp: 242-249.
  • [15] Ernst, E. 2004. On the existence of Positive Eigenvalues for the Isotropic Linear Elasticity System with Negative Shear Modulus. Commun. Part Diff. Eq., 29: 1745 – 1753.
  • [16] Faierman, M., Fries RJ., Mennicken, R., Möller, M. 2000. On the essential spectrum of the linearized Navier-Stokes operator. Integr. Equat. Oper. Th., 38: 9-27.
  • [17] Kozhevnikov, A. 1986. On the operator of the linearized steady-state Navier-Stokes problem. (English. Russian original), Math. USSR, Sb. 53, 1- 16; translation from Mat. Sb., Nov. Ser., 125: 3-18 (1984).
  • [18] Kozhevnikov, A. 1989. On the second and third boundary value problems of the static elasticity theory. Sov. Math. Dokl., 38: 427-430.
  • [19] Kozhevnikov, A. 1993. The basic boundary value problems of static elasticity theory and their Cosserat spectrum. Math. Z., 213: 241-274.
  • [20] Kozhevnikov, A. 1996. On the first stationary boundary-value problem of elasticity in weighted Sobolev spaces in exterior domains of R3. Appl. Math. Optim., 34: 183-190.
  • [21] Kozhevnikov, A., Skubachevskaya, T. 1997. Some applications of pseudo-differential operators to elasticity. Hokkaido Math. J., 26: 297- 322.
  • [22] Kozhevnikov, A., Lepsky, O. 1998. Power series solutions to basic stationary boundary value problems of elasticity. Integr. Equat. Oper. Th., 31: 449-469.
  • [23] Kozhevnikov, A. 1999. A history of the Cosserat spectrum. In The Maz'ya anniversary collection (Vol. 1 Rostock,), Operator Theory: A. M. S. A., 109: 223-234.
  • [24] Kozhevnikov, A. 2000. On a Lower Bound of the Cosserat Spectrum for the Second Boundary Value Problem of Elastostatics, Boundary Value Problem of Elastostatics, Applicable Analysis. An Int. J., 74: 301-309.
  • [25] Kucher,VA., Markenschoff, X., Paukshto, MV. 2004. The (-1) Cosserat Eigenfunctions for Spherical Geometry with Application to Poroelasticity. Math. Mech. Solids, 9: 399-410.
  • [26] Kucher, VA., Markenscoff, X. 2004. The Cosserat eigenfunctions for the elliptic exterior problem with applications to thermoelasticity and Stokes flow. Z. Angew. Math. Phys., 55, 1065- 1073.
  • [27] Levitin, MR. 1992. On the spectrum of a generalized Cosserat problem. C.R. Acad. Sci. Paris, 315, 925-930.
  • [28] Liu, W., Markenscoff, X. 1998. The Cosserat Spectrum Theory in Thermoelasticity and Application to the Problem of Heat Flow Past a Rigid Spherical Inclusion. J. Appl. Mech., 65: 614- 618.
  • [29] Liu, W. 1998. The Cosserat spectrum theory and its applications, University of California, San Diego and San Diego State University, PhD thesis.
  • [30] Liu, W., Plotkin, A. 1999. Application of the Cosserat Spectrum Theory to Stokes Flow. J. Appl. Mech., 66, 811-814.
  • [31] Liu, W., Markenscoff, X., Paukshto, M. 1999. The Cosserat spectrum theory for twodimensional thermoelastic problems. J. Therm. Stresses, 22: 225 - 239.
  • [32] Liu, W., Markenscoff, X., Paukshto, M. 1999. The Discrete Cosserat Eigenfunctions for a Spherical Shell. J. Elasticity, 52: 239-255.
  • [33] Liu, W., Markenscoff, X., Paukshto, M. 1999. The Cosserat Subspace ũ(-1) for Bodies of Spherical Geometry, Physics and Astronomy. J. Elasticity, 54: 113-128.
  • [34] Liu, W., Markenscoff, X. 2000. The Cosserat spectrum for cylindrical geometries: (Part 1: discrete subspace). Int. J. Solids Struct., 37: 1165- 1176.
  • [35] Liu, W., Markenscoff, X. 2000. The Cosserat spectrum for cylindrical geometries: (Part 2: u(-1) subspace and applications). Int. J. Solids Struct., 37: 1177-1190.
  • [36] Liu, W., Plotkin, A. 2000. Application of Cosserat-spectrum theory to the weakly compressible Stokes flow past a sphere. J. Eng. Math., 38: 155-172.
  • [37] Markenscoff, X., Paukshto, M. 1995. The correspondence between cavities and rigid inclusions in three-dimensional elasticity and the cosserat spectrum. Int. J. Solids Struct., Special topics in the theory of elastic: A volume in honour of Professor John Dundurs, 32: 431-438.
  • [38] Markenscoff, X., Paukshto, M. 1996. On the Cavities and Rigid Inclusions Correspondence and the Cosserat Spectrum. Math. Nachr., 177: 183-188.
  • [39] Markenscoff, X., Paukshto, MV. 1998. The Cosserat spectrum in the theory of elasticity and applications. Proc. R. Soc. Lond. A, 454: 631-643.
  • [40] Markenscoff, X., Liu, W., Paukshto, M. 1998. Application of the cosserat spectrum theory to viscoelasticity. J. Mech. Phys. Solids, 46: 1969-1980.
  • [41] Markenscoff, X. 2006. Stress Independence of Poisson's Ratio and Divergence-Free Body Forces. J. Elasticity, 83: 65-74.
  • [42] Maz'ya, VG., Mikhlin, SG. 1967. The Cosserat spectrum of the equations of the theory of elasticity. Vestnik Leningrad Univ. Math., 22: 58-63
  • [43] Mikhlin, SG. 1966. On the Cosserat functions, in Problems of mathematical analysis. Leningrad State University, 59-69.
  • [44] Mikhlin, SG. 1967. Further investigation of Cosserat functions. Vestnik Leningrad Univ. Math., 22: 96-102.
  • [45] Mikhlin, SG. 1970. Some properties of the Cosserat spectrum of spatial and plane problems of the theory of elasticity. Vestnik Leningrad Univ. Math., 25: 31-45.
  • [46] Mikhlin, SG. 1970. The Cosserat spectrum of static problems of the theory of elasticity and its application. In: Problemy mekhaniki tverdogo deformiruemogo tela (Problems of the mechanics of a solid deformable body). Sudostroenie, Leningrad, pp. 265-271.
  • [47] Mikhlin, SG. 1973. The spectrum of a family of operators in the theory of elasticity. Russ. Math. Surveys, 28: 45-88; translation from Uspekhi Mat. Nauk, 28: 43-82.
  • [48] Mikhlin, SG. 1973. The Cosserat spectrum of problems of the theory of elasticity for infinite domains (Russian). In: Issledovaniya po uprugosti i plastichnosti ( Studies in elasticity and plasticity). Izdat. Leningrad Univ., 149: 41-50.
  • [49] Mikhlin, SG., Morozov, NF., Paukshto, MV. 1995. The integral equations of the theory of elasticity, Teubner-Texte zur Mathematik. 135. Leipzig: Teubner Verlagsges. 375 p.
  • [50] Ol'shanskii, MA., Chizhonkov, EV. 2000. On the best constant in the inf-sup-condition for enlongated rectangular domains. Math. Notes, 67: 325-332.
  • [51] Paukshto, M. 1997. On Some Applications of Integral Equations in Elasticity, (Proc. of 4th Int. Conference in Integral Methods in Science and Engineering, IMSE 96, 1996, Oulu, Finland), Integral methods in science and engineering, Volume 1, analytic methods. Pitman Res. Notes Math. Ser., 374: 9-17.
  • [52] Pelissier, MC. 1975. Rèsolution numèrique de quelques problèmes raides en mècanique des milieux faiblement compressibles. Calcolo, 12: 275-314
  • [53] Pobedrya, BE. 2007. Approximation methods in viscoelasticity theory. Russ. J. Math. Phys.,14: 110- 114.
  • [54] Riedl, T. 2010. Cosserat Operators of Higher Order and Applications, Universität Bayreuth, PhD thesis.
  • [55] Sherman, DI. 1938. Sur la distribution des nombres caractéristiques d'équations intégrales du problème plan de la théorie d'élasticité. (Russian) Publ. Inst. Séismol. Acad. Sci. URSS, 82: 1-24
  • [56] Simader, CG., Weyers, S. 2006. An operator related to the Cosserat spectrum. Applications. Analysis, 26: 169-198.
  • [57] Simader, CG., Wahl, W. 2006. Introduction to the Cosserat problem. Analysis, 26: 1-7.
  • [58] Simader, CG. 2006. The weak L^{q}-Cosserat spectrum for the first boundary value problem in the half-space. Applications to Stokes' and Lamé's system. Analysis, 26: 9-84.
  • [59] Simader, CG. 2009. The Cosserat problem related to the curl and a complete characterization of all solenoidal vector fields vanishing at the boundary in case of space dimension n=2. Analysis, 29: 355-364.
  • [60] Simader, CG. 2011. Weak L²-solutions to a Stokes-like system of fourth order in bounded Lipschitz domains. Appl. Anal., 90: 215 – 226.
  • [61] Simader, CG. 2010. A New Approach to the Regularity of Weak Lq-Solutions of Stokes and Similar Equations via the Cosserat Operator. Advances in Mathematical Fluid Mechanics, pp. 553-572.
  • [62] Valeev, VE. 2000. The Cosserat spectrum of a boundary-value problem of elasticity theory. (English. Russian original) Vestn. St. Petersbg. Univ., Math., 33: 10-15; translation from Vestn. StPeterbg. Univ., Ser. I, Mat. Mekh. Astron., 3: 14-21, 2000.
  • [63] Velte, W. 1990. On optimal constants in some inequalities. The Navier-Stokes equations theory and numerical methods, Proc. Conf., Oberwolfach/FRG , Lect. Notes Math., 1431: 158- 168.
  • [64] Velte, W. 1996. On inequalities of Friedrichs and Babuška-Aziz. Meccanica, 31: 589- 596.
  • [65] Velte, W. 1998. On inequalities of Friedrichs and Babuška-Aziz in dimension three. Z. Anal. Anwend., 17: 843-857.
  • [66] Weyers, S. 2006. L^{q}-solutions to the Cosserat spectrum in bounded and exterior domains. Analysis, 26: 85-167.
  • [67] Zernov, V., Pichugin, AV., Kaplunov, J. 2006. Eigenvalue of a semi-infinite elastic strip. Proc. R. Soc., 462: 1255-1270.

A short history of the Cosserat spectrum problem

Yıl 2011, Cilt: 1 Sayı: 1, 55 - 58, 01.01.2011

Yüksel Soykan Melih Göcen

Öz

The aim of this paper is to give a short review about Cosserat spectrum.

Anahtar Kelimeler

Cosserat spectrum Cosserat eigenvalues Dirichlet problem

Kaynakça

  • [1]Bakhvalov, NS., Knyazev, AV., Parashkevov, R R. 2002. Extension theorems for Stokes and Lamé equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficients. Numer. Linear Algebr., 9: 115-139.
  • [2]Chizhonkov, EV. 1994. Application of the Cosserat spectrum to the optimization of a method for solving the Stokes problem. Russ. J. Numer. Anal. M., 9: 191-199.
  • [3] Chizhonkov, EV. 2009. Numerical solution to a stokes interface problem. Comp. Math., 49: 105- 116.
  • [4] Cosserat, E., Cosserat, F. 1898. Sur les èquations de la thèorie de l'èlasticitè. C. R. Acad. Sci. (Paris), 126: 1089-1091.
  • [5] Cosserat, E., Cosserat, F. 1898. Sur les fonctions potentielles de la thèorie de l'èlasticitè. C. R. Acad. Sci. (Paris), 126: 1129-1132.
  • [6] Cosserat, E., Cosserat, F. 1898. Sur la dèformation infiniment petite d'un ellipsoide èlastique. C. R. Acad. Sci. (Paris), 127: 315-318.
  • [7] Cosserat, E., Cosserat, F. 1902. Sur la solution des èquations de l'èlasticitè dans le cas où les valeurs des inconnues à la frontière sont donnèes. C. R. Acad. Sci. (Paris), 133: 145-147.
  • [8] Cosserat, E., Cosserat, F. 1902. Sur une application des fonctions potentielles de la thèorie de l'èlasticitè. C. R. Acad. Sci. (Paris), 133: 210-213
  • [9] Cosserat, E., Cosserat, F. 1902. Sur la dèformation infiniment petite d'un corps èlastique soumis à des forces donnèes. C. R. Acad. Sci. (Paris), 133: 271-273.
  • [10] Cosserat, E., Cosserat, F. 1902. Sur la dèformation infiniment petite d'une enveloppe sphèrique èlastique. C. R. Acad. Sci. (Paris), 133: 326-329.
  • [11] Cosserat, E., Cosserat, F. 1902. Sur la dèformation infiniment petite d'un ellipsoide èlastique soumis à des efforts donnèes sur la frontière. C. R. Acad. Sci. (Paris), 133: 361-364.
  • [12] Cosserat, E., Cosserat, F. 1902. Sur un point critique particulier de la solution des èquations de l'èlasticitè dans le cas où les efforts sur la frontière sont donnèes. C. R. Acad. Sci. (Paris), 133: 382-384.
  • [13] Costabel, M., Dauge. 2000. M. On the Cosserat spectrum in polygons and polyhedra, IRMAR Conference, Lausanne.
  • [14] Crouzeix, M. 1997. On an operator related to the convergenceof Uzawa's algorithm for the Stokes equation. In: M. O. Bristeau, G. Etgen, W. Fitzgibbon, J. L. Lions, J. Pèriaux and M. F. Wheeler, editors, Computational Science for the 21st Century, Wiley, Chichester, pp: 242-249.
  • [15] Ernst, E. 2004. On the existence of Positive Eigenvalues for the Isotropic Linear Elasticity System with Negative Shear Modulus. Commun. Part Diff. Eq., 29: 1745 – 1753.
  • [16] Faierman, M., Fries RJ., Mennicken, R., Möller, M. 2000. On the essential spectrum of the linearized Navier-Stokes operator. Integr. Equat. Oper. Th., 38: 9-27.
  • [17] Kozhevnikov, A. 1986. On the operator of the linearized steady-state Navier-Stokes problem. (English. Russian original), Math. USSR, Sb. 53, 1- 16; translation from Mat. Sb., Nov. Ser., 125: 3-18 (1984).
  • [18] Kozhevnikov, A. 1989. On the second and third boundary value problems of the static elasticity theory. Sov. Math. Dokl., 38: 427-430.
  • [19] Kozhevnikov, A. 1993. The basic boundary value problems of static elasticity theory and their Cosserat spectrum. Math. Z., 213: 241-274.
  • [20] Kozhevnikov, A. 1996. On the first stationary boundary-value problem of elasticity in weighted Sobolev spaces in exterior domains of R3. Appl. Math. Optim., 34: 183-190.
  • [21] Kozhevnikov, A., Skubachevskaya, T. 1997. Some applications of pseudo-differential operators to elasticity. Hokkaido Math. J., 26: 297- 322.
  • [22] Kozhevnikov, A., Lepsky, O. 1998. Power series solutions to basic stationary boundary value problems of elasticity. Integr. Equat. Oper. Th., 31: 449-469.
  • [23] Kozhevnikov, A. 1999. A history of the Cosserat spectrum. In The Maz'ya anniversary collection (Vol. 1 Rostock,), Operator Theory: A. M. S. A., 109: 223-234.
  • [24] Kozhevnikov, A. 2000. On a Lower Bound of the Cosserat Spectrum for the Second Boundary Value Problem of Elastostatics, Boundary Value Problem of Elastostatics, Applicable Analysis. An Int. J., 74: 301-309.
  • [25] Kucher,VA., Markenschoff, X., Paukshto, MV. 2004. The (-1) Cosserat Eigenfunctions for Spherical Geometry with Application to Poroelasticity. Math. Mech. Solids, 9: 399-410.
  • [26] Kucher, VA., Markenscoff, X. 2004. The Cosserat eigenfunctions for the elliptic exterior problem with applications to thermoelasticity and Stokes flow. Z. Angew. Math. Phys., 55, 1065- 1073.
  • [27] Levitin, MR. 1992. On the spectrum of a generalized Cosserat problem. C.R. Acad. Sci. Paris, 315, 925-930.
  • [28] Liu, W., Markenscoff, X. 1998. The Cosserat Spectrum Theory in Thermoelasticity and Application to the Problem of Heat Flow Past a Rigid Spherical Inclusion. J. Appl. Mech., 65: 614- 618.
  • [29] Liu, W. 1998. The Cosserat spectrum theory and its applications, University of California, San Diego and San Diego State University, PhD thesis.
  • [30] Liu, W., Plotkin, A. 1999. Application of the Cosserat Spectrum Theory to Stokes Flow. J. Appl. Mech., 66, 811-814.
  • [31] Liu, W., Markenscoff, X., Paukshto, M. 1999. The Cosserat spectrum theory for twodimensional thermoelastic problems. J. Therm. Stresses, 22: 225 - 239.
  • [32] Liu, W., Markenscoff, X., Paukshto, M. 1999. The Discrete Cosserat Eigenfunctions for a Spherical Shell. J. Elasticity, 52: 239-255.
  • [33] Liu, W., Markenscoff, X., Paukshto, M. 1999. The Cosserat Subspace ũ(-1) for Bodies of Spherical Geometry, Physics and Astronomy. J. Elasticity, 54: 113-128.
  • [34] Liu, W., Markenscoff, X. 2000. The Cosserat spectrum for cylindrical geometries: (Part 1: discrete subspace). Int. J. Solids Struct., 37: 1165- 1176.
  • [35] Liu, W., Markenscoff, X. 2000. The Cosserat spectrum for cylindrical geometries: (Part 2: u(-1) subspace and applications). Int. J. Solids Struct., 37: 1177-1190.
  • [36] Liu, W., Plotkin, A. 2000. Application of Cosserat-spectrum theory to the weakly compressible Stokes flow past a sphere. J. Eng. Math., 38: 155-172.
  • [37] Markenscoff, X., Paukshto, M. 1995. The correspondence between cavities and rigid inclusions in three-dimensional elasticity and the cosserat spectrum. Int. J. Solids Struct., Special topics in the theory of elastic: A volume in honour of Professor John Dundurs, 32: 431-438.
  • [38] Markenscoff, X., Paukshto, M. 1996. On the Cavities and Rigid Inclusions Correspondence and the Cosserat Spectrum. Math. Nachr., 177: 183-188.
  • [39] Markenscoff, X., Paukshto, MV. 1998. The Cosserat spectrum in the theory of elasticity and applications. Proc. R. Soc. Lond. A, 454: 631-643.
  • [40] Markenscoff, X., Liu, W., Paukshto, M. 1998. Application of the cosserat spectrum theory to viscoelasticity. J. Mech. Phys. Solids, 46: 1969-1980.
  • [41] Markenscoff, X. 2006. Stress Independence of Poisson's Ratio and Divergence-Free Body Forces. J. Elasticity, 83: 65-74.
  • [42] Maz'ya, VG., Mikhlin, SG. 1967. The Cosserat spectrum of the equations of the theory of elasticity. Vestnik Leningrad Univ. Math., 22: 58-63
  • [43] Mikhlin, SG. 1966. On the Cosserat functions, in Problems of mathematical analysis. Leningrad State University, 59-69.
  • [44] Mikhlin, SG. 1967. Further investigation of Cosserat functions. Vestnik Leningrad Univ. Math., 22: 96-102.
  • [45] Mikhlin, SG. 1970. Some properties of the Cosserat spectrum of spatial and plane problems of the theory of elasticity. Vestnik Leningrad Univ. Math., 25: 31-45.
  • [46] Mikhlin, SG. 1970. The Cosserat spectrum of static problems of the theory of elasticity and its application. In: Problemy mekhaniki tverdogo deformiruemogo tela (Problems of the mechanics of a solid deformable body). Sudostroenie, Leningrad, pp. 265-271.
  • [47] Mikhlin, SG. 1973. The spectrum of a family of operators in the theory of elasticity. Russ. Math. Surveys, 28: 45-88; translation from Uspekhi Mat. Nauk, 28: 43-82.
  • [48] Mikhlin, SG. 1973. The Cosserat spectrum of problems of the theory of elasticity for infinite domains (Russian). In: Issledovaniya po uprugosti i plastichnosti ( Studies in elasticity and plasticity). Izdat. Leningrad Univ., 149: 41-50.
  • [49] Mikhlin, SG., Morozov, NF., Paukshto, MV. 1995. The integral equations of the theory of elasticity, Teubner-Texte zur Mathematik. 135. Leipzig: Teubner Verlagsges. 375 p.
  • [50] Ol'shanskii, MA., Chizhonkov, EV. 2000. On the best constant in the inf-sup-condition for enlongated rectangular domains. Math. Notes, 67: 325-332.
  • [51] Paukshto, M. 1997. On Some Applications of Integral Equations in Elasticity, (Proc. of 4th Int. Conference in Integral Methods in Science and Engineering, IMSE 96, 1996, Oulu, Finland), Integral methods in science and engineering, Volume 1, analytic methods. Pitman Res. Notes Math. Ser., 374: 9-17.
  • [52] Pelissier, MC. 1975. Rèsolution numèrique de quelques problèmes raides en mècanique des milieux faiblement compressibles. Calcolo, 12: 275-314
  • [53] Pobedrya, BE. 2007. Approximation methods in viscoelasticity theory. Russ. J. Math. Phys.,14: 110- 114.
  • [54] Riedl, T. 2010. Cosserat Operators of Higher Order and Applications, Universität Bayreuth, PhD thesis.
  • [55] Sherman, DI. 1938. Sur la distribution des nombres caractéristiques d'équations intégrales du problème plan de la théorie d'élasticité. (Russian) Publ. Inst. Séismol. Acad. Sci. URSS, 82: 1-24
  • [56] Simader, CG., Weyers, S. 2006. An operator related to the Cosserat spectrum. Applications. Analysis, 26: 169-198.
  • [57] Simader, CG., Wahl, W. 2006. Introduction to the Cosserat problem. Analysis, 26: 1-7.
  • [58] Simader, CG. 2006. The weak L^{q}-Cosserat spectrum for the first boundary value problem in the half-space. Applications to Stokes' and Lamé's system. Analysis, 26: 9-84.
  • [59] Simader, CG. 2009. The Cosserat problem related to the curl and a complete characterization of all solenoidal vector fields vanishing at the boundary in case of space dimension n=2. Analysis, 29: 355-364.
  • [60] Simader, CG. 2011. Weak L²-solutions to a Stokes-like system of fourth order in bounded Lipschitz domains. Appl. Anal., 90: 215 – 226.
  • [61] Simader, CG. 2010. A New Approach to the Regularity of Weak Lq-Solutions of Stokes and Similar Equations via the Cosserat Operator. Advances in Mathematical Fluid Mechanics, pp. 553-572.
  • [62] Valeev, VE. 2000. The Cosserat spectrum of a boundary-value problem of elasticity theory. (English. Russian original) Vestn. St. Petersbg. Univ., Math., 33: 10-15; translation from Vestn. StPeterbg. Univ., Ser. I, Mat. Mekh. Astron., 3: 14-21, 2000.
  • [63] Velte, W. 1990. On optimal constants in some inequalities. The Navier-Stokes equations theory and numerical methods, Proc. Conf., Oberwolfach/FRG , Lect. Notes Math., 1431: 158- 168.
  • [64] Velte, W. 1996. On inequalities of Friedrichs and Babuška-Aziz. Meccanica, 31: 589- 596.
  • [65] Velte, W. 1998. On inequalities of Friedrichs and Babuška-Aziz in dimension three. Z. Anal. Anwend., 17: 843-857.
  • [66] Weyers, S. 2006. L^{q}-solutions to the Cosserat spectrum in bounded and exterior domains. Analysis, 26: 85-167.
  • [67] Zernov, V., Pichugin, AV., Kaplunov, J. 2006. Eigenvalue of a semi-infinite elastic strip. Proc. R. Soc., 462: 1255-1270.
Toplam 67 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Yüksel Soykan Bu kişi benim

Melih Göcen Bu kişi benim

Yayımlanma Tarihi 1 Ocak 2011
Yayımlandığı Sayı Yıl 2011 Cilt: 1 Sayı: 1

Kaynak Göster

APA Soykan, Y., & Göcen, M. (2011). A short history of the Cosserat spectrum problem. Karaelmas Fen Ve Mühendislik Dergisi, 1(1), 55-58.
AMA Soykan Y, Göcen M. A short history of the Cosserat spectrum problem. Karaelmas Fen ve Mühendislik Dergisi. Ocak 2011;1(1):55-58.
Chicago Soykan, Yüksel, ve Melih Göcen. “A Short History of the Cosserat Spectrum Problem”. Karaelmas Fen Ve Mühendislik Dergisi 1, sy. 1 (Ocak 2011): 55-58.
EndNote Soykan Y, Göcen M (01 Ocak 2011) A short history of the Cosserat spectrum problem. Karaelmas Fen ve Mühendislik Dergisi 1 1 55–58.
IEEE Y. Soykan ve M. Göcen, “A short history of the Cosserat spectrum problem”, Karaelmas Fen ve Mühendislik Dergisi, c. 1, sy. 1, ss. 55–58, 2011.
ISNAD Soykan, Yüksel - Göcen, Melih. “A Short History of the Cosserat Spectrum Problem”. Karaelmas Fen ve Mühendislik Dergisi 1/1 (Ocak 2011), 55-58.
JAMA Soykan Y, Göcen M. A short history of the Cosserat spectrum problem. Karaelmas Fen ve Mühendislik Dergisi. 2011;1:55–58.
MLA Soykan, Yüksel ve Melih Göcen. “A Short History of the Cosserat Spectrum Problem”. Karaelmas Fen Ve Mühendislik Dergisi, c. 1, sy. 1, 2011, ss. 55-58.
Vancouver Soykan Y, Göcen M. A short history of the Cosserat spectrum problem. Karaelmas Fen ve Mühendislik Dergisi. 2011;1(1):55-8.