2/25/2011

Luis Silvestre
Chicago

On unique continuation for nonlinear elliptic equations

We will discuss the following issue: if two solutions of a nonlinear elliptic equation coincide in a small ball, do they necessarily coincide everywhere? The problem is fairly well understood in the linear setting, but it is open for most interesting nonlinear elliptic equations. We will analyze the difficulties of the problem and prove a result in arguably the simplest case in which one cannot linearize the equation a priori.