Besov regularity in non-linear generalized functions

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 represen...

Besov Regularity for the Stokes Problem

This paper is concerned with regularity estimates for the solutions to the Stokes problem in polygonal domains in R 2 : Especially, we derive regularity results in speciic scales of Besov spaces which arise in connection with adaptive numerical schemes. The proofs of the main results are based on representations of the solution spaces which were given by Osborn 20] and on characterizations of B...

Constructing Generalized Mean Functions Using Convex Functions with Regularity Conditions

The generalized mean function has been widely used in convex analysis and mathematical programming. This paper studies a further generalization of such a function. A necessary and sufficient condition is obtained for the convexity of a generalized function. Additional sufficient conditions that can be easily checked are derived for the purpose of identifying some classes of functions which guar...

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 in R d and its relationship with adaptive and other nonlinear methods for approximating these solutions. The smoothness spaces which determine the eeciency of such nonlinear approximation in L p (() are the Besov spaces B (L (()), := (=d + 1=p) ?1. Thus, the regularity of the so...

Direct Search Generalized Simplex Algorithm for Optimizing Non-linear Functions