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

Abstract

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.