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

2019/04/11 by Di Fratta, Giovanni, Fiorenza, Alberto · 2 citations
#35B65 (Secondary) #35D30 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.05839

Abstract

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.

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• Nonlinear scalar field equations with a critical Hardy potential
• A Survey on the Div-Curl Lemma and Some Extensions to Fractional Sobolev Spaces

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