Vol. 7, No. 8, 2014

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Stochastic homogenization of viscous Hamilton–Jacobi equations and applications

Scott N. Armstrong and Hung V. Tran

Vol. 7 (2014), No. 8, 1969–2007
Abstract

We present stochastic homogenization results for viscous Hamilton–Jacobi equations using a new argument that is based only on the subadditive structure of maximal subsolutions (i.e., solutions of the “metric problem”). This permits us to give qualitative homogenization results under very general hypotheses: in particular, we treat nonuniformly coercive Hamiltonians that satisfy instead a weaker averaging condition. As an application, we derive a general quenched large deviation principle for diffusions in random environments and with absorbing random potentials.

Keywords
stochastic homogenization, Hamilton–Jacobi equation, quenched large deviation principle, diffusion in random environment, weak coercivity, degenerate diffusion
Mathematical Subject Classification 2010
Primary: 35B27
Milestones
Received: 13 May 2014
Accepted: 7 October 2014
Published: 5 February 2015
Authors
Scott N. Armstrong
Centre de Recherche en Mathématiques de la Décision
Université Paris-Dauphine
Place du Maréchal de Lattre de Tassigny
75775 Paris 16
France
Hung V. Tran
Department of Mathematics
The University of Chicago
5734 South University Avenue
Chicago, IL 60637
United States