Regularity estimates for elliptic boundary value problems in Besov spaces

Authors:
Constantin Bacuta;James H. Bramble;Jinchao Xu
Affiliations:
Dept. of Mathematics, The Pennsylvania State University, University Park, Pennsylvania;Department of Mathematics, Texas A & M University, College Station, Texas;Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania
Venue:
Mathematics of Computation
Year:
2003

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Abstract

We consider the Dirichlet problem for Poisson's equation on a nonconvex plane polygonal domain Ω. New regularity estimates for its solution in terms of Besov and Sobolev norms of fractional order are proved. The analysis is based on new interpolation results and multilevel representations of norms on Sobolev and Besov spaces. The results can be extended to a large class of elliptic boundary value problems. Some new sharp finite element error estimates are deduced.