Upper bounds for the eigenvalues of Hessian equations

We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equationsComment: 15 pages, 1 figur

Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type

The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow

A monotonicity result for the first Steklov-Dirichlet Laplacian eigenvalue

In this paper, we consider the first Steklov-Dirichlet eigenvalue of the Laplace operator in annular domain with a spherical hole. We prove a monotonicity result with respect the hole when the outer region is centrally symmetrc