Besov regularity for solutions of p-harmonic equations

Abstract

We establish the higher fractional differentiability of the solutions to nonlinear elliptic equations in divergence form, i.e., divA(x, Du) = div F, when A is a p-harmonic type operator, and under the assumption that x → A(x, ζ) belongs to the critical Besov-Lipschitz space B an/a,q∗ We prove that some fractional differentiability assumptions on F transfer to Du with no losses in the natural exponent of integrability. When div F = 0, we show that an analogous extra differentiability property for Du holds true under a Triebel- Lizorkin assumption on the partial map x → A(x, ζ).