Shape Derivatives of Boundary Integral Operators in Electromagnetic Scattering. Part I: Shape Differentiability of Pseudo-homogeneous Boundary Integral Operators

被引:32
作者
Costabel, Martin [1 ]
Le Louer, Frederique [2 ]
机构
[1] Univ Rennes 1, IRMAR, Inst Math, F-35042 Rennes, France
[2] Univ Gottingen, Inst Numer & Andgewandte Math, D-37083 Gottingen, Germany
关键词
Boundary integral operators; Pseudo-homogeneous kernels; Fundamental solution; Surface differential operators; Shape derivatives; Sobolev spaces; FRECHET DIFFERENTIABILITY;
D O I
10.1007/s00020-012-1954-z
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth deformations of the boundary. We prove that the boundary integral operators are infinitely differentiable without loss of regularity. The potential operators are infinitely shape differentiable away from the boundary, whereas their derivatives lose regularity near the boundary. We study the shape differentiability of surface differential operators. The shape differentiability properties of the usual strongly singular or hypersingular boundary integral operators of interest in acoustic, elastodynamic or electromagnetic potential theory can then be established by expressing them in terms of integral operators with weakly singular kernels and of surface differential operators.
引用
收藏
页码:509 / 535
页数:27
相关论文
共 26 条
[1]  
[Anonymous], 2001, ACOUSTIC ELECTROMAGN
[2]  
[Anonymous], 1983, Lecture Notes in Math.
[3]  
[Anonymous], 1979, N HOLLAND SERIES APP
[4]  
[Anonymous], 1992, SPRINGER SERIES COMP
[5]  
[Anonymous], 1980, MATH MONOGR
[6]   On the Frechet differentiability of boundary integral operators in the inverse elastic scattering problem [J].
Charalambopoulos, A .
INVERSE PROBLEMS, 1995, 11 (06) :1137-1161
[7]  
Colton D., 1998, APPL MATH SCI
[8]   Shape Derivatives of Boundary Integral Operators in Electromagnetic Scattering. Part II: Application to Scattering by a Homogeneous Dielectric Obstacle [J].
Costabel, Martin ;
Le Louer, Frederique .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2012, 73 (01) :17-48
[9]  
DELABOURDONNAYE A, 1993, CR ACAD SCI I-MATH, V316, P369
[10]  
Delfour M.C., 2001, LECT NOTES PURE APPL, V216