A short proof of local regularity of distributional solutions of Poisson’s equation

Di Fratta, Giovanni; Fiorenza, Alberto

doi:10.1090/proc/14895

A short proof of local regularity of distributional solutions of Poisson’s equation
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by Giovanni Di Fratta and Alberto Fiorenza PDF

Proc. Amer. Math. Soc. 148 (2020), 2143-2148 Request permission

Abstract:

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

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