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Second-Order Differential Operators with Non-Local Ventcel's Boundary Conditions

Year 2019, Volume: 2 Issue: 4, 144 - 152, 01.12.2019
https://doi.org/10.33205/cma.574194

Abstract

Different boundary conditions have been introduced for second-order differential operators and the properties of the operators on the corresponding domains have been deeply investigated since the work of Feller. The aim of this paper is to study second-order differential operators satisfying a Ventcel's type boundary condition which involves simultaneously both the endpoints of a real interval. We study different general properties and a resolvent estimate for this kind of operators.

Thanks

Work performed under the auspices of G.N.A.M.P.A. (Indam)

References

  • [1] F. Altomare, M. Campiti, Korovkin-type Approximation Theory and its Applications, De Gruyter Studies in Mathematics 17, W. De Gruyter, Berlin-New York, 1994.
  • [2] F. Altomare, M. Cappelletti Montano, V. Leonessa and I. Ra¸sa, Markov Operators, Positive Semigroups and Approximation Processes, de Gruyter Studies in Mathematics 61, de Gruyter, Berlin/Boston, 2014.
  • [3] A. Attalienti, M. Campiti, Semigroups generated by ordinary differential operators in L1(I), Positivity 8 (1) (2004), 11–30.
  • [4] M. Campiti, S. P. Ruggeri, Approximation of semigroups and cosine functions in spaces of periodic functions, Applicable Analysis 86 (2) (2007), 167–186.
  • [5] Ph. Clément, C. A. Timmermans, On C0-semigroups generated by differential operators satisfying Ventcel’s boundary conditions, Indag. Math. 89 (1986), 379–387.
  • [6] K.-J. Engel, R. Nagel, One-parameter semigroups for linear evolution equations, Graduate Text in Mathematics 194, Springer, New York, 2000.
  • [7] W. Feller, The parabolic differential equations and the associated semi-groups of transformations, Annals of Math. 55 (3) (1952), 468–519.
  • [8] P. Mandl, Analytical treatment of one-dimensional Markov processes, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 151, Springer-Verlag, Berlin-Heidelberg-New York, 1969.
  • [9] C. A. Timmermans, On C0-semigroups in a space of bounded continuous functions in the case of entrance or natural boundary points. In: Gòmez-Fernandez J.A., Guerra-Vázquez F., Lòpez-Lagomasino G., Jiménez-Pozo M.A. (eds). Approximation and Optimization, Lecture Notes in Mathematics, 1354. Springer, Berlin, Heidelberg, 2006.
Year 2019, Volume: 2 Issue: 4, 144 - 152, 01.12.2019
https://doi.org/10.33205/cma.574194

Abstract

References

  • [1] F. Altomare, M. Campiti, Korovkin-type Approximation Theory and its Applications, De Gruyter Studies in Mathematics 17, W. De Gruyter, Berlin-New York, 1994.
  • [2] F. Altomare, M. Cappelletti Montano, V. Leonessa and I. Ra¸sa, Markov Operators, Positive Semigroups and Approximation Processes, de Gruyter Studies in Mathematics 61, de Gruyter, Berlin/Boston, 2014.
  • [3] A. Attalienti, M. Campiti, Semigroups generated by ordinary differential operators in L1(I), Positivity 8 (1) (2004), 11–30.
  • [4] M. Campiti, S. P. Ruggeri, Approximation of semigroups and cosine functions in spaces of periodic functions, Applicable Analysis 86 (2) (2007), 167–186.
  • [5] Ph. Clément, C. A. Timmermans, On C0-semigroups generated by differential operators satisfying Ventcel’s boundary conditions, Indag. Math. 89 (1986), 379–387.
  • [6] K.-J. Engel, R. Nagel, One-parameter semigroups for linear evolution equations, Graduate Text in Mathematics 194, Springer, New York, 2000.
  • [7] W. Feller, The parabolic differential equations and the associated semi-groups of transformations, Annals of Math. 55 (3) (1952), 468–519.
  • [8] P. Mandl, Analytical treatment of one-dimensional Markov processes, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 151, Springer-Verlag, Berlin-Heidelberg-New York, 1969.
  • [9] C. A. Timmermans, On C0-semigroups in a space of bounded continuous functions in the case of entrance or natural boundary points. In: Gòmez-Fernandez J.A., Guerra-Vázquez F., Lòpez-Lagomasino G., Jiménez-Pozo M.A. (eds). Approximation and Optimization, Lecture Notes in Mathematics, 1354. Springer, Berlin, Heidelberg, 2006.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Michele Campıtı 0000-0003-3794-1878

Publication Date December 1, 2019
Published in Issue Year 2019 Volume: 2 Issue: 4

Cite

APA Campıtı, M. (2019). Second-Order Differential Operators with Non-Local Ventcel’s Boundary Conditions. Constructive Mathematical Analysis, 2(4), 144-152. https://doi.org/10.33205/cma.574194
AMA Campıtı M. Second-Order Differential Operators with Non-Local Ventcel’s Boundary Conditions. CMA. December 2019;2(4):144-152. doi:10.33205/cma.574194
Chicago Campıtı, Michele. “Second-Order Differential Operators With Non-Local Ventcel’s Boundary Conditions”. Constructive Mathematical Analysis 2, no. 4 (December 2019): 144-52. https://doi.org/10.33205/cma.574194.
EndNote Campıtı M (December 1, 2019) Second-Order Differential Operators with Non-Local Ventcel’s Boundary Conditions. Constructive Mathematical Analysis 2 4 144–152.
IEEE M. Campıtı, “Second-Order Differential Operators with Non-Local Ventcel’s Boundary Conditions”, CMA, vol. 2, no. 4, pp. 144–152, 2019, doi: 10.33205/cma.574194.
ISNAD Campıtı, Michele. “Second-Order Differential Operators With Non-Local Ventcel’s Boundary Conditions”. Constructive Mathematical Analysis 2/4 (December 2019), 144-152. https://doi.org/10.33205/cma.574194.
JAMA Campıtı M. Second-Order Differential Operators with Non-Local Ventcel’s Boundary Conditions. CMA. 2019;2:144–152.
MLA Campıtı, Michele. “Second-Order Differential Operators With Non-Local Ventcel’s Boundary Conditions”. Constructive Mathematical Analysis, vol. 2, no. 4, 2019, pp. 144-52, doi:10.33205/cma.574194.
Vancouver Campıtı M. Second-Order Differential Operators with Non-Local Ventcel’s Boundary Conditions. CMA. 2019;2(4):144-52.