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Stochastic
homogenization of viscous Hamilton–Jacobi equations and
applications
Scott N. Armstrong and Hung V. Tran |
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Vol. 7 (2014), No. 8, 1969–2007
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 35B27
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Milestones
Received: 13 May 2014
Accepted: 7 October 2014
Published: 5 February 2015
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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 |
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| Hung V. Tran | |
| Department of Mathematics The University of Chicago 5734 South University Avenue Chicago, IL 60637 United States |
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