Shape derivatives of boundary integral operators in electromagnetic scattering. Part I: Shape differentiability of pseudo-homogeneous boundary integral operators. - Archive ouverte HAL Access content directly
Journal Articles Integral Equations and Operator Theory Year : 2012

Shape derivatives of boundary integral operators in electromagnetic scattering. Part I: Shape differentiability of pseudo-homogeneous boundary integral operators.

Abstract

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.
Fichier principal
Vignette du fichier
CoFLL_shape_derivatives_Part_I_rev.pdf (270.26 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00592280 , version 1 (11-05-2011)
hal-00592280 , version 2 (29-02-2012)

Identifiers

Cite

Martin Costabel, Frédérique Le Louër. Shape derivatives of boundary integral operators in electromagnetic scattering. Part I: Shape differentiability of pseudo-homogeneous boundary integral operators.. Integral Equations and Operator Theory, 2012, 72 (4), pp.509-535. ⟨10.1007/s00020-012-1954-z⟩. ⟨hal-00592280v2⟩
280 View
618 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More