Maximal mean exit time related to the p-Laplace operator

In this paper we introduce a boundary value problem involving powers of the p-Laplace operator. We will then prove a variant of Talenti inequality which shows that the Schwarz symmetrization of the solution of the boundary value problem is majorized by the solution of the appropriately symmetrized version of the problem. The case of equality is also investigated. Finally, as an application, we will consider an optimization problem related to the mean exit time of a Wiener process and derive a symmetry result.