On the stochastic Evans-Aronsson problem

by D. Gomes, H. Sanchez-Morgado
Refereed Journals Year: 2014


D. Gomes H. Sanchez-Morgado, On the stochastic Evans-Aronsson problem, Transactions of the AMS. 366 (2014), no. 2, 903-929. 


In this paper the stochastic version of the Evans-Aronsson problem is studied. Both for the mechanical case and two dimensional problems we prove the existence of smooth solutions. We establish that the corresponding effective Lagrangian and Hamiltonian are smooth. We study the limiting behavior and the convergence of the effective Lagrangian and Hamiltonian, Mather measures and minimizers. We end the paper with applications to stationary mean-field games.


1088-6850(online) ISSN 0002-9947(print)


Stochastic Evans-Aronsson Mean field games Non-coercive variational problems