Approximation numbers of embeddings of Sobolev spaces
Under appropriate hypotheses on the domain \(\Omega\) in \(\mathbb{R}^{2m}\), upper bounds for the approximation numbers of the compact embeddings of \(\mathring H^m(\Omega)\) in \(L_q(\Omega)\) \((q\geq 2)\) and in a suitable Orlicz space are obtained in terms of eigenvalues of \((- \Delta)^m\) with zero Dirichlet conditions. The case of Neumann boundary conditions is also discussed, as is the situation when these embeddings are not compact.
scientific article; zbMATH DE number 861943