Regularity of the $p$-Poisson equation in the plane

Erik Lindgren; Peter Lindqvist

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arXiv · 1311.6795

Regularity of the $p$-Poisson equation in the plane

Erik Lindgren·Peter Lindqvist

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Abstract

We study the regularity of the $p$-Poisson equation $$ Δ_p u = h, \quad h\in L^q $$ in the plane. In the case $p>2$ and $2<q<\infty$ we obtain the sharp Hölder exponent for the gradient. In the other cases we come arbitrarily close to the sharp exponent.

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Erik Lindgren, Peter Lindqvist. 2013-12-13. Regularity of the $p$-Poisson equation in the plane. https://arxiv.org/abs/1311.6795

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