Mather measures for space–time periodic nonconvex Hamiltonians

Ponente(s): Eddaly Guerra Velasco

Diogo Gomes developed techniques and tools with the purpose of extending the Aubry-Mather theory in a stochastic setting. These results were also extended in the time-dependent setting. However to construct analogs to the Aubry-Mather measures for nonconvex Hamiltonians it is necessary to use the adjoint method introduced by L. Evans and H. V. Tran, the construction of the measures was made by F. Cagnetti, D. Gomes, and H. V. Tran. The main goal of this talk is to give a construction of Mather measures for space-time periodical nonconvex Hamiltonians using analog techniques. Moreover, we also will prove that there is only one value, such that the viscous Hamilton–Jacobi equation has a smooth periodic solution unique up to an additive constant.