Compactness of embeddings of function spaces on quasi-bounded domains and the distribution of eigenvalues of related elliptic operators. Part II

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:429

Article

Leopold, Hans-Gerd¹  Skrzypczak, Leszek² 

[1] Univ Jena, Math Inst, D-07740 Jena, Germany

[2] Adam Mickiewicz Univ, Fac Math & Comp Sci, PL-61614 Poznan, Poland

关键词: Compact embeddings;    Besov and Triebel-Lizorkin spaces;    Quasi-bounded domains;    Elliptic operators;    Distribution of eigenvalues;   

DOI  :  10.1016/j.jmaa.2015.03.072

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free