Shift Theorems for the Biharmonic Dirichlet Problem

Constantin Bacuta (), James H. Bramble () and Joseph E. Pasciak ()
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Constantin Bacuta: The Pennsyvania State University, Dept. of Mathematics
James H. Bramble: Texas A & M University, Dept. of Mathematics
Joseph E. Pasciak: Texas A & M University, Dept. of Mathematics

A chapter in Recent Progress in Computational and Applied PDES, 2002, pp 1-26 from Springer

Abstract: Abstract 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 R 2 are used in the proof of the interpolation theorem.

Keywords: interpolation spaces; biharmonic operator; shift theorems (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-0113-8_1

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DOI: 10.1007/978-1-4615-0113-8_1

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