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Bernstein estimates for systems of weakly coupled fully non-linear elliptic equations and integral operators

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Mercoledi' 24 febbraio alle ore 12 in aula 2BC/30 TA Gabriele Terrone (Universidade Tecnica de Lisboa) terra' un seminario dal titolo "Bernstein estimates for systems of weakly coupled fully non-linear
elliptic equations and integral operators".

-Abstract
Bernstein estimates permit to bound the sup-norm of the gradient of the solution with the sup-norm of the solution. We are particularly interested in systems that arise in the stochastic optimal control problems of hybrid systems, that are systems of weakly coupled nonlinear elliptic equations. Our techniques can also be adapted to handle nonlocal integral operators, such as the factional Laplacian. In both cases, a generalization of Bernstein estimates for first and second derivatives of classical solutions will be presented. In the light of the approach of Caffarelli-Cabré, Bernstein estimates follow rather simply by the maximum principle for the linearized operator associated to the nonlinear problem.

This is a joint work with Diogo Gomes.

Rif. int. M. Bardi, A. Cesaroni, P. Mannucci

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