Subspace Interpolation with Applications to Elliptic Regularity |
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Authors: | Constantin Bacuta |
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Institution: | 1. Mathematical Sciences, University of Delaware , Newark, Delaware, USA bacuta@math.udel.edu |
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Abstract: | In this paper, we prove new embedding results by means of subspace interpolation theory and apply them to establishing regularity estimates for the biharmonic Dirichlet problem and for the Stokes and the Navier–Stokes systems on polygonal domains. The main result of the paper gives a stability estimate for the biharmonic problem at the threshold index of smoothness. The classic regularity estimates for the biharmonic problem are deduced as a simple corollary of the main result. The subspace interpolation tools and techniques presented in this paper can be applied to establishing sharp regularity estimates for other elliptic boundary value problems on polygonal domains. |
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Keywords: | Biharmonic operator Elliptic regularity Navier–Stokes systems Subspace interpolation Shift theorems Stokes systems Threshold index of smoothness |
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