A stochastic Evans-Aronsson problem

Diogo Gomes; Héctor Sánchez Morgado

doi:10.1090/S0002-9947-2013-05936-3

A stochastic Evans-Aronsson problem

Diogo Gomes, Héctor Sánchez Morgado

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	903-929
Number of pages	27
Journal	Transactions of the American Mathematical Society
Volume	366
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-2013-05936-3
State	Published - 2014

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-2013-05936-3

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title = "A stochastic Evans-Aronsson problem",

abstract = "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.",

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AB - 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.

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JO - Transactions of the American Mathematical Society

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A stochastic Evans-Aronsson problem

Abstract

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