# Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations

created by dragoni on 18 Jul 2017

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Submitted Paper

Inserted: 18 jul 2017
Last Updated: 18 jul 2017

Year: 2017

ArXiv: 1707.00553 PDF

Abstract:

We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable. We look at Hamiltonians like $H(x,\sigma(x)p,\omega)$ where $\sigma(x)$ is a matrix associated to a Carnot group. The rescaling considered is consistent with the underlying Carnot group structure, thus anisotropic. We will prove that under suitable assumptions for the Hamiltonian, the solutions of the $\varepsilon$-problem converge to a deterministic function which can be characterized as the unique (viscosity) solution of a suitable deterministic Hamilton-Jacobi problem.

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