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Transactions of the American Mathematical Society

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A stochastic Evans-Aronsson problem

Authors: Diogo Gomes and Héctor Sánchez Morgado
Journal: Trans. Amer. Math. Soc. 366 (2014), 903-929
MSC (2010): Primary 49L99
Published electronically: August 8, 2013
MathSciNet review: 3130321
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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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Additional Information

Diogo Gomes
Affiliation: Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, Lisboa, Portugal

Héctor Sánchez Morgado
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, México DF 04510, México

Received by editor(s): November 9, 2011
Received by editor(s) in revised form: June 1, 2012
Published electronically: August 8, 2013
Additional Notes: The first author was partially supported by CAMGSD-LARSys through FCT Program POCTI-FEDER and by grants PTDC/MAT/114397/2009, UTAustin/MAT/0057/2008, and UTA-CMU/MAT/0007/2009
The second author is grateful to the Instituto Superior Técnico for its hospitality
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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