Regularity and well posedness for the Laplace operator on polyhedral domains

Constantin Bacuta; Victor Nistor; Ludmil Zikatanov

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Regularity and well posedness for the Laplace operator on polyhedral domains

Constantin Bacuta·Victor Nistor·Ludmil Zikatanov

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Abstract

We announce a well-posedness result for the Laplace equation in weighted Sobolev spaces on polyhedral domains in $\RR^n$ with Dirichlet boundary conditions. The weight is the distance to the set of singular boundary points. We give a detailed sketch of the proof in three dimensions.

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Constantin Bacuta, Victor Nistor, Ludmil Zikatanov. 2004-10-07. Regularity and well posedness for the Laplace operator on polyhedral domains. https://arxiv.org/abs/math/0410207

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