Calculus of Variations and Geometric Measure Theory

G. Di Fratta - A. Fiorenza

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

created by difratta on 30 Apr 2021


Published Paper

Inserted: 30 apr 2021
Last Updated: 30 apr 2021

Journal: Proc. Amer. Math. Soc.
Volume: 148
Year: 2020

ArXiv: 1904.05839 PDF


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-Fr\'echet representation theorem.