A new embedding result for Kondratiev spaces and application to adaptive approximation of elliptic PDEs

Abstract

In a continuation of recent work on Besov regularity of solutions to elliptic PDEs in Lipschitz domains with polyhedral structure, we prove an embedding between weighted Sobolev spaces (Kondratiev spaces) relevant for the regularity theory for such elliptic problems, and TriebelLizorkin spaces, which are known to be closely related to approximation spaces for nonlinear n-term wavelet approximation. Additionally, we also provide necessary conditions for such embeddings. As a further application we discuss the relation of these embedding results with results by Gaspoz and Morin for approximation classes for adaptive Finite element approximation, and subsequently apply these result to parametric problems.