We examine the p-harmonic equation div |grad u|(p-2). grad u = mu, where mu is a bounded Radon measure. We determine a range of p's for which solutions to the equation verify an a priori estimate. For such p's we also prove a higher integrability result.
It is shown that the approximating equations whose existence is required in the author's previous work on partially regular weak solutions can be constructed without any additional assumption about the equation itself. This leads to a variation of a Galerkin method.
We prove higher integrability for the gradient of bounded minimizers of some variational integrals with anisotropic growth.