Stochastic homogenization of viscous Hamilton-Jacobi equations and applications

Abstract

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

37 pages

References in corpus (2)

• Quenched large deviations for random walk in a random environment
• Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations

Cited by in corpus (8)

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• Quenched large deviations for simple random walks on percolation models including long-range correlations
• Stochastic Homogenization for Reaction-Diffusion Equations
• Homogenization of a class of one-dimensional nonconvex viscous Hamilton-Jacobi equations with random potential
• Stochastic homogenization of certain nonconvex Hamilton-Jacobi equations
• Min-max formulas and other properties of certain classes of nonconvex effective Hamiltonians
• Quenched large deviations for brownian motion in a random potential