Inserted: 20 jul 2016
Last Updated: 9 mar 2017
Journal: Commun. Contemp. Math.
Pages: 22 pages
We consider local weak solutions of the Poisson equation for the $p-$Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-hand side. The result comes with a local scaling invariant a priori estimate.
Keywords: fractional Sobolev spaces, regularity of solutions, Degenerate quasilinear elliptic equations, higher differentiability