G. Di Fratta, A. Fiorenza:

"A short proof of local regularity of distributional solutions of Poisson's equation";

in: "ASC Report 10/2019", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2019, ISBN: 978-3-902627-12-4, 1 - 8.

We prove a local regularity result for distributional solutions of the Poisson's equation with $L^p$ data. We use a very short argument based on Weyl's lemma and Riesz-Fréchet representation theorem.

http://www.asc.tuwien.ac.at/preprint/2019/asc10x2019.pdf

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