Comptes Rendus
no. 9
Partial differential equations/Functional analysis
On the regularity of solutions to Poisson's equation
[Sur la régularité des solutions de l'équation de Poisson]

Présenté par : the Editorial Board

Rahul Garg1 ; Daniel Spector1, 2
1 Technion – Israel Institute of Technology, Department of Mathematics, Haifa, Israel
2 National Chiao Tung University, Department of Applied Mathematics, Hsinchu, Taiwan
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 819-823.

Dans cette note, nous annonçons de nouveaux résultats de régularité pour des solutions distributionelles localement intégrables à l'équation de Poisson. Cela comprend, par exemple, les solutions standard obtenues par convolution avec la solution fondamentale. En particulier, nos résultats montrent qu'il n'y a aucune différence qualitative de régularité entre ces solutions dans le plan et celles en dimensions supérieures.

In this note, we announce new regularity results for some locally integrable distributional solutions to Poisson's equation. This includes, for example, the standard solutions obtained by convolution with the fundamental solution. In particular, our results show that there is no qualitative difference in the regularity of these solutions in the plane and in higher dimensions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.07.001

Rahul Garg 1 ; Daniel Spector 1, 2

1 Technion – Israel Institute of Technology, Department of Mathematics, Haifa, Israel
2 National Chiao Tung University, Department of Applied Mathematics, Hsinchu, Taiwan 
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Rahul Garg; Daniel Spector. On the regularity of solutions to Poisson's equation. Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 819-823. doi : 10.1016/j.crma.2015.07.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.07.001/

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