Uniqueness for Hamilton-Jacobi equations with discontinuous coefficients

Pierpaolo Soravia Dipartimento di Matematica Pura e Applicata

                     e-mail soravia@math.unipd.it

In this talk we will discuss a class of fully nonlinear degenerate elliptic equations with discontinuous coefficients. Viscosity solutions can be defined and are an appropriate notion of solution, but in general boundary value problems have multiple solutions. We will point out appropriate assumptions on the data that allow to obtain a comparison principle and a unique solution.