Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-02T22:03:57.654Z Has data issue: false hasContentIssue false
  • English
  • Français

MAXWELL'S EQUATIONS AND DIELECTRIC OBSTACLES WITH LIPSCHITZ BOUNDARIES

Published online by Cambridge University Press:  01 February 1998

RODOLFO H. TORRES
RODOLFO H. TORRES
Affiliation:
Department of Mathematics, 405 Snow Hall, University of Kansas, Lawrence, Kansas 66045-2142, USA
Get access

Abstract

The classical transmission problem for the scattering of time-harmonic electromagnetic waves by a dielectric object is solved using layer potential techniques. The surface of the object is only assumed to be a Lipschitz manifold. Unlike in the case of smoother surfaces, neither the calculus of pseudodifferential operators nor the compactness of certain boundary operators are available tools. Nevertheless, the particular representation of the solutions and the choice of the space of boundary data used in the paper make the problem tractable via harmonic analysis techniques for elliptical partial differential equations in nonsmooth domains.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 157 - 169
Copyright
The London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)