We prove the simmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In case of Poisson equation, our proof is alternative to the onesâ€¦ (More)

Following a new approach to overdetermined problems we prove that Serrinâ€™s result is stable under suitable perturbations of the boundary conditions, even without a priori estimates of the regularityâ€¦ (More)

Recently, following a new approach, the symmetry of the solutions to overdetermined problems has been established for a class of Hessian type operators. In this paper we prove that the radialâ€¦ (More)

Let be a smooth, convex, unbounded domain of R . Denote by 1( ) the Â…rst nontrivial Neumann eigenvalue of the Hermite operator in ; we prove that 1( ) 1. The result is sharp since equality sign isâ€¦ (More)

We establish a pointwise comparison result for a nonlinear degenerate elliptic Dirichlet problem using an isoperimetric inequality involving the total mean curvature. In particular this resultâ€¦ (More)