Hardy inequalities for pp-Laplacians with Robin boundary conditions

In this paper we study the best constant in a Hardy inequality for the pp-Laplace operator on convex domains with Robin boundary conditions. We show, in particular, that the best constant equals ((p−1)/p)p((p−1)/p)p whenever Dirichlet boundary conditions are imposed on a subset of the boundary of non-zero measure. We also discuss some generalizations to non-convex domains.