Open AccessA stochastic Evans-Aronsson problem
Author(s) -
Diogo A. Gomes,
Héctor Sánchez Morgado
Publication year - 2013
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-2013-05936-3
Subject(s) - mathematics , lagrangian , hamiltonian (control theory) , limiting , convergence (economics) , hamiltonian system , mathematical analysis , mathematical optimization , mechanical engineering , engineering , economics , economic growth
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.