Eigenvalue distribution of semi-elliptic operators in anisotropic Sobolev spaces
This paper begins by introducing some basic notation and concepts used in the study of anisotropic spaces. It then proceeds to formulate some definitions, after which it lists some important properties of anisotropic function spaces of Besov and Sobolev type. The paper then deals with the concepts of anisotropic \(d\)-sets, and the approximation numbers of related embeddings and trace operators. The paper concludes by giving two-sided estimates for the asymptotic behaviour of the eigenvalues for a semi-elliptic differential operator, and of a special trace operator on an anisotropic \(d\)-set.
scientific article; zbMATH DE number 5550897
scientific article