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Published in:
2002 | OriginalPaper | Chapter
Shift Theorems for the Biharmonic Dirichlet Problem
Authors : Constantin Bacuta, James H. Bramble, Joseph E. Pasciak
Published in: Recent Progress in Computational and Applied PDES
Publisher: Springer US
Included in: Professional Book Archive
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We consider the biharmonic Dirichlet problem on a polygonal domain. Regularity estimates in terms of Sobolev norms of fractional order are proved. The analysis is based on new interpolation results which generalizes Kellogg’s method for solving subspace interpolation problems. The Fourier transform and the construction of extension operators to Sobolev spaces on R2 are used in the proof of the interpolation theorem.