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

Salani, Paolo

Annales de l'I.H.P. 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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