Besov regularity for elliptic boundary value problems

This paper studies the regularity of solutions to boundary value problems for Laplace's equation on Lipschitz domains\Ω in R d and its relationship with adaptive and other nonlinear methods for approximating these solutions. The smoothness spaces which determine the efficiency of such nonlinear approximation in L p(\Ω\Γ are the Besov spaces B ff ø (L ø(\Ω\Γ16 ø := (ff=d + 1=p) \Γ1 . Thus, the regularity of the solution in this scale of Besov spaces is investigated with the aim of determining the largest ff for which the solution is in B ff ø (L ø(\Ω\Γ21 The regularity theorems given in this paper build upon the recent results of Jerison and Kenig [JK]. The proof of the regularity theorem uses characterizations of Besov spaces by wavelet expansions. Key Words: Besov spaces, elliptic boundary value problems, potential theory, adaptive methods, nonlinear approximation, wavelets AMS Subject classification: primary 35B65, secondary 31B10, 41A46, 46E...