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Title: Weyl Type Bound on Positive Interior Transmission Eigenvalues
Author: Lakshtanov, Evgeny
Vainberg, Boris
Keywords: Counting function
Interior transmission eigenvalues
Weyl formula
Issue Date: Apr-2014
Publisher: Taylor & Francis
Abstract: This paper contains a lower bound of the Weyl type on the counting function of the positive eigenvalues of the interior transmission eigenvalue problem which justifies the existence of an infinite set of positive interior transmission eigenvalues. We consider the classical transmission problem as well as the case where the inhomogeneous medium contains an obstacle. One of the essential components of the proof is an estimate for the D-t-N operator for the Helmholtz equation for positive λ that replaces the standard parameter-elliptic estimate valid outside of the positive semi-axis.
Peer review: yes
DOI: 10.1080/03605302.2014.881853
ISSN: 0036-1410
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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