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

Salani, Paolo

Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 32 (2015) no. 4, pp. 763-783

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.

Keywords: Rearrangements, Elliptic equations, Infimal convolution, Power concave envelope, Minkowski addition of convex sets

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