Combination and mean width rearrangements of solutions to elliptic equations in convex sets

Abstract

We introduce a method to compare solutions of different equations in different domains. As a consequence, we define a new kind of rearrangement which applies to solution of fully nonlinear equations $F(x,u,Du,D^{2}u)=0$, not necessarily in divergence form, in convex domains and we obtain Talenti's type results for this kind of rearrangement.