DISTRIBUTIONAL DERIVATIVES ON A REGULAR OPEN SURFACE WITH PHYSICAL APPLICATIONS

Yıl 2011, Cilt: 01 Sayı: 2, 203 - 222, 01.12.2011

Burak Polat

Öz

The spatial derivatives of Schwartz-Sobolev distributions which display singularities of arbitrary order on an arbitrary regular open surface are investigated. The contributions of the present investigation to literature are i an approach alternative to the derivation of the distributional derivatives of multilayers by Estrada and Kanwal; ii an extension of the available results for closed surfaces to open surfaces featuring boundary distributions of arbitrary order. The end results are applied in the distributional investigation of Maxwell equations in presence of single and double layer sources located on a regular open surface.

Anahtar Kelimeler

Schwartz-Sobolev distributions, vector analysis, electromagnetic theory, boundary relations, single and double layer structures

Kaynakça

• Estrada, R. and Kanwal, R.P., (1980), Applications of distributional derivatives to wave propagation, J.Inst.Math.Appl., 26, 39-63.
• Kanwal, R.P., (2004), Generalized Functions: Theory and Technique, 3rd Ed., Birkhauser Boston.
• Estrada, R. and Kanwal, R.P., (1985), Distributional analysis of discontinuous fields, J.Math. Anal. Appl., 105, 478-490.
• Friedlander, G. and Joshi, M., (1998), Introduction to the Theory of Distributions, 2nd Ed., Cambridge University Press.
• Friedman, A., (1963), Generalized Functions and Partial Differential Equations, Dover Publ.
• Weatherburn, C.E., (1925), On differential invariants in geometry of surfaces, with some applications to mathematical physics, Quarterly Journal of Mathematics, 230-269.
• Weatherburn, C.E., (1927), Differential Geometry of Three Dimensions,Vol.1, Cambridge University Press.
• Farassat, F., (1977), Discontinuities in aerodynamics and aeroacoustics, the concepts and applications of generalized functions, J. Sound Vib., 55, 165-193.
• Wang, L.Q., Xu, M.T. and Wei, X.H., (2008), Multiscale Theorems, Advances in Chemical Engineer- ing, 34, 175-468.
• Betounes, D., (1982), Nonclassical fields with singularities on a moving surface, J.Math Phys., 23, 12, 2311.
• Estrada, R. and Kanwal, R.P., (1987), Higher order fundamental forms of a surface and their applica- tions to wave propagation and generalized derivatives, Rendiconti del Circolo Matematico di Palermo
• Serie II, Tomo XXXVI, 27-62. Van Bladel, J., (1985), Electromagnetic Fields, Hemisphere Publishing Corporation.