Stochastic homogenization of nonconvex Hamilton-Jacobi equations: a counterexample

Abstract

We provide an example of a Hamilton-Jacobi equation in which stochastic homogenization does not occur. The Hamiltonian involved in this example satisfies the standard assumptions of the literature, except that it is not convex.

References in corpus (4)

• Stochastic homogenization of viscous Hamilton-Jacobi equations and applications
• Shortest spanning trees and a counterexample for random walks in random environments
• A Sublinear Variance Bound for Solutions of a Random Hamilton Jacobi Equation
• A Partial Homogenization Result for Nonconvex Viscous Hamilton-Jacobi Equations

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