Regularity for the biharmonic problem and the Stokes systems on polygonal domains

Constantin Bacuta
Department of Mathematics
University of Deleware

Abstract: We consider the biharmonic Dirichlet problem on a polygonal domain. New regularity estimates in terms of Sobolev-Besov norms of fractional order are proved. The analysis is based on new interpolation results which generalizes Kellogg's method for solving subspace interpolation problems. We apply our results to establish regularity estimates for the Stokes system.