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

Erik Lindgren; Peter Lindqvist

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

Analysis of PDEs 2013-12-16 v2

Authors: Erik Lindgren , Peter Lindqvist

Abstract

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

Keywords

p-Poisson equation regularity theory Hölder exponent gradient estimates plane nonlinear elliptic equations

Cite

@article{arxiv.1311.6795,
  title  = {Regularity of the $p$-Poisson equation in the plane},
  author = {Erik Lindgren and Peter Lindqvist},
  journal= {arXiv preprint arXiv:1311.6795},
  year   = {2013}
}

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14 pages

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