Besov Regularity for Interface Problems

This paper is concerned with the Besov regularity of the solutions to interface problems in a segment S of the unit disk in R 2 : We investigate the smoothness of the solutions as measured in the speciic scale B s (L (S)); 1== = s=2+1=p; of Besov spaces which determines the order of approximation that can be achieved by adap-tive and nonlinear numerical schemes. The proofs are based on representations of the solution spaces which were derived by Kellogg 15] and on characterizations of Besov spaces by wavelet expansions.