Partial differential equations/Functional analysis
On the regularity of solutions to Poisson's equation
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 819-823.

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.

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.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2015.07.001
Garg, Rahul 1; Spector, Daniel 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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Garg, Rahul; Spector, Daniel. 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. http://www.numdam.org/articles/10.1016/j.crma.2015.07.001/

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