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Poster communications

Regularity results for elliptic problems with measure

Abstract : In this work, we study the solution of the Laplace equation: \[ -\Delta u =g \delta_\sigma\;\;\;\hbox{ in } Q\subseteq \mathbb{R}^3, \] where \(\delta_\sigma\) is the Dirac mass on a crack \(\sigma\) of \(Q\) and \(g\in L^2(\sigma)\). First, we discuss the existence and the uniqueness of a solution in \(W^{1,p}(Q)\) for \(p<2\) (due to the Dirac mass, the right-hand side is not in \(H^{-1}(Q)\)). Then, we prove the regularity of the solution and a priori estimates in weighted Sobolev spaces.
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Poster communications
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https://hal-uphf.archives-ouvertes.fr/hal-03142664
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Submitted on : Tuesday, February 16, 2021 - 11:11:35 AM
Last modification on : Saturday, October 9, 2021 - 3:15:38 AM

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  • HAL Id : hal-03142664, version 1

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Sadjiya Ariche, Colette de Coster, Serge Nicaise. Regularity results for elliptic problems with measure. Nord Pas-de-Calais/Belgium congress of mathematics, Oct 2013, Valenciennes, France. ⟨hal-03142664⟩

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