Strongly oscillating singularities for the interior transmission eigenvalue problem

Anne Sophie Bonnet Ben Dhia, Lucas Chesnel

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)

Abstract

In this paper, we investigate a two-dimensional interior transmission eigenvalue problem for an inclusion made of a composite material. We consider configurations where the difference between the parameters of the composite material and those of the background changes sign on the boundary of the inclusion. In a first step, under some assumptions on the parameters, we extend the variational approach of the T-coercivity to prove that the transmission eigenvalues form at most a discrete set. In the process, we also provide localization results. Then, we study what happens when these assumptions are not satisfied. The main idea is that, due to very strong singularities that can occur at the boundary, the problem may lose Fredholmness in the natural H 1 framework. Using Kondratiev theory, we propose a new functional framework where the Fredholm property is restored.

Original languageEnglish
Article number104004
JournalInverse Problems
Volume29
Issue number10
DOIs
Publication statusPublished - Oct 2013
MoE publication typeA1 Journal article-refereed

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