Regularity results for elliptic problems with measure - Archive ouverte HAL Access content directly
Poster Communications Year :

Regularity results for elliptic problems with measure

(1) , (1) , (1)
1

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.
Not file

Dates and versions

hal-03142664 , version 1 (16-02-2021)

Identifiers

  • HAL Id : hal-03142664 , version 1

Cite

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⟩
8 View
0 Download

Share

Gmail Facebook Twitter LinkedIn More