Strongly oscillating singularities for the interior transmission eigenvalue problem

Anne Sophie Bonnet Ben Dhia, Lucas Chesnel

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

8 Sitaatiot (Scopus)

Abstrakti

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.

AlkuperäiskieliEnglanti
Artikkeli104004
JulkaisuInverse Problems
Vuosikerta29
Numero10
DOI - pysyväislinkit
TilaJulkaistu - lokakuuta 2013
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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