Besov regularity for elliptic boundary value problems

Abstract

This paper studies the regularity of solutions to boundary value problems forLaplace's equation on LipschitzdomainsOmegain Rdand its relationship with adaptiveand other nonlinear methods for approximating these solutions. The smoothnessspaces which determine the efficiency of such nonlinear approximation in L p(OmegaGammaare the Besov spaces Bff?(L ?(OmegaGamma16 ? := (ff=d + 1=p)Gamma1. Thus, the regularity of thesolution in this scale of Besov spaces is investigated ...