SHARP BOUNDS FOR THE FIRST EIGENVALUE AND THE TORSIONAL RIGIDITY RELATED TO SOME ANISOTROPIC OPERATORS

Abstract

In this paper we prove a sharp upper bound for the first Dirichlet eigenvalue of a class of nonlinear elliptic operators which includes the operator , that is the p ‐Laplacian, and , namely the pseudo‐ p ‐Laplacian. Moreover we prove a stability result by means of a suitable isoperimetric deficit. Finally, we give a sharp lower bound for the anisotropic p ‐torsional rigidity.