On the use of \(T\)-coercivity to study the interior transmission eigenvalue problem
The paper is devoted to the study of the so-called interior transmission problem (in the scalar case when the contrast in the scattering medium occurs in two independent functions) by developing the \(T\)-coercivity approach; cf. [\textit{A. S. Bonnet-Ben Dhia}, \textit{P. Ciarlet jun.} and \textit{C. M. Zwölf}, J. Comput. Appl. Math. 234, No. 6, 1912--1919 (2010; Zbl 1202.78026); erratum \textit{A. S. Bonnet-Ben Dhia} and \textit{P. Ciarlet jun.}, ibid. 234, No. 8, 2616 (2010; Zbl 1266.78026)]. The authors obtain conditions to ensure the Fredholm property of the operator associated with the problem and prove that the set of interior transmission eigenvalues is discrete. Change sign situations of the difference between the inclusion index and the background index are included in this study, and consequent Faber-Krahn type inequalities are obtained.
scientific article; zbMATH DE number 5919175