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2014 Stochastic homogenization of viscous Hamilton–Jacobi equations and applications
Scott Armstrong, Hung Tran
Anal. PDE 7(8): 1969-2007 (2014). DOI: 10.2140/apde.2014.7.1969

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.

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Scott Armstrong. Hung Tran. "Stochastic homogenization of viscous Hamilton–Jacobi equations and applications." Anal. PDE 7 (8) 1969 - 2007, 2014. https://doi.org/10.2140/apde.2014.7.1969

Information

Received: 13 May 2014; Accepted: 7 October 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1320.35033
MathSciNet: MR3318745
Digital Object Identifier: 10.2140/apde.2014.7.1969

Subjects:
Primary: 35B27

Keywords: degenerate diffusion , Diffusion in random environment , Hamilton–Jacobi equation , quenched large deviation principle , Stochastic homogenization , weak coercivity

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.7 • No. 8 • 2014
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