Calculus of Variations and Geometric Measure Theory

R. Garg - D. Spector

On regularity of solutions to Poisson's equation

created by spector on 31 Mar 2014
modified on 12 Oct 2015


C. R. Acad. Sci. Paris Sér. I Math.

Inserted: 31 mar 2014
Last Updated: 12 oct 2015

Year: 2014


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.