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.
This work was partially supported by the National Science Foundation under Grant DMS-9973328.
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Bacuta, C., Bramble, J.H., Pasciak, J.E. (2002). Shift Theorems for the Biharmonic Dirichlet Problem. In: Chan, T.F., Huang, Y., Tang, T., Xu, J., Ying, LA. (eds) Recent Progress in Computational and Applied PDES. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0113-8_1
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DOI: https://doi.org/10.1007/978-1-4615-0113-8_1
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