Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 429, Issue 1, Pages 439-460Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2015.03.072
Keywords
Compact embeddings; Besov and Triebel-Lizorkin spaces; Quasi-bounded domains; Elliptic operators; Distribution of eigenvalues
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We prove the asymptotic behaviour of eigenvalues of elliptic self-adjoint differential operators defined on a wide class of quasi-bounded domains. The estimates are based on corresponding asymptotic behaviour of entropy numbers of Sobolev embeddings of Sobolev and Besov function spaces defined on the quasi-bounded domains. We consider also the inverse problem i.e. we identify the class of functions that can describe the asymptotic behaviour of eigenvalues of Dirichlet Laplacian of some quasi-bounded domain. (C) 2015 Elsevier Inc. All rights reserved.
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