Electromagnetic scattering on nonsmooth domains

Sdes with Oblique Reflections on Nonsmooth Domains

It has been pointed out by Weining Kang and Ruth Williams that there is an error in an argument in [1]. The purpose of this note is to correct the argument. The error affects only Case 2 of the paper, and occurs in the first display at the top of page 580, at the end of the proof of Theorem 5.1. This display claims that a certain bound follows from (3.28) of the paper, and implicitly assumes th...

The Electromagnetic Inverse Scattering Problem for Partially Coated Lipschitz Domains

We consider the inverse scattering problem of determining the shape of a partially coated obstacle in R 3 from a knowledge of the incident time harmonic electromagnetic plane wave and the electric far field pattern of the scattered wave. A justification is given of the linear sampling method in this case and numerical examples are provided showing the practicality of our method. 1. Introduction...

An analysis of electromagnetic scattering from finite-width strips

On Serrin’s symmetry result in nonsmooth domains and its applications

The goal of this paper is to show that Serrin’s result on overdetermined problems holds true for symmetric non-smooth domains. Specifically, we show that if a non-smooth domain D satisfies appropriate symmetry and convexity assumptions, and there exists a positive solution to a general overdetermined problem on D, then D must be a ball. As an application, we improve results on symmetry of non-n...

Potential Theoretic Characterizations of Nonsmooth Domains

A large number of works have been devoted to the study of potential theory for nonsmooth domains, such as Lipschitz domains, NTA domains, uniform domains, John domains and Hölder domains, since the pioneering works of Carleson [12] and Hunt-Wheeden [18, 19] for Lipschitz domains. Among them, the boundary Harnack principle (abbreviated to BHP) and the identification of the Martin boundary played...