# [CvGmt News] Seminario Davini (03/05/2016)

Alfonso Sorrentino sorrentino at mat.uniroma2.it
Thu Apr 28 10:29:57 CEST 2016

SEMINARIO DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Università degli Studi di Roma "Tor Vergata"

Martedi' 3 Maggio 2016, ore 14:30 Aula dal Passo

Andrea Davini (Sapienza, Universita' degli Studi di Roma)

Title: Convergence of the solutions of the discounted H-J equation

Abstract:
We consider a continuous coercive Hamiltonian on the cotangent bundle of
the compact connected manifold $M$ which is convex in the momentum. We
prove that the viscosity solutions $u_\lambda:M\to\R$ of the critical
Hamilton-Jacobi equation with discount factor $\lambda>0$ converge
uniformly, as $\lambda$ goes to 0, to a specific solution $u_0:M\to\R$ of
the limit equation. We characterize $u_0$ in terms of Peierls barrier and
projected Mather measures. As a corollary, we infer that the ergodic
approximation, as introduced by Lions, Papanicolaou and Varadhan in 1987
in their seminal paper on periodic homogenization of Hamilton-Jacobi
equations, selects a specific corrector in the limit. The talk is based on
a joint work with A. Fathi, R. Iturriaga and M. Zavidovique that will
appear on Inventiones Mathematicae.

Website: http://www.mat.uniroma2.it/~castorin/Seminario-PDE.html

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