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

Erik Lindgren, Peter Lindqvist

Published 2013-11-26, updated 2013-12-13Version 2

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.