Calculus of Variations and Geometric Measure Theory

A. Davini

Stochastic homogenization of a class of quasiconvex and possibly degenerate viscous HJ equations in 1d

created by davini on 27 Mar 2024
modified on 28 Mar 2024


Accepted Paper

Inserted: 27 mar 2024
Last Updated: 28 mar 2024

Journal: J. Convex Anal.
Year: 2024

ArXiv: 2402.17031 PDF


We prove homogenization for possibly degenerate viscous Hamilton-Jacobi equations with a Hamiltonian of the form $G(p)+V(x,\omega)$, where $G$ is a quasiconvex, locally Lipschitz function with superlinear growth, the potential $V(x,\omega)$ is bounded and Lipschitz continuous, and the diffusion coefficient $a(x,\omega)$ is allowed to vanish on some regions or even on the whole $\mathbb{R}$. The class of random media we consider is defined by an explicit scaled hill condition on the pair $(a,V)$ which is fulfilled as long as the environment is not ``rigid''.