Regularity of the p-Poissson Equation in the Plane

Abstract

We study the regularity of the p-Poisson equation Δpu=h,h∈Lq, Δpu=h,h∈Lq, in the plane. In the case p > 2 and 2 < q < ∞, we obtain the sharp Hölder exponent for the gradient. In the other cases, we come arbitrarily close to the sharp exponent.