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

Erik Lindgren, Peter Lindqvist

We study the regularity of the $p$-Poisson equation $${\Delta }_{p}u=h,h\in L^q$$ in the plane. In the case $p>2$ and $2<q<\infty$ we obtain the sharp Hölder exponent for the gra…