2017/04/25 by Pierre Cardaliaguet, Panagiotis E. Souganidis, Cardaliaguet, Pierre +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1704.07602
openalex publication_date 2017/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove, under some assumptions, the existence of correctors for the\nstochastic homoge-nization of of " viscous " possibly degenerate\nHamilton-Jacobi equations in stationary ergodic media. The general claim is\nthat, assuming knowledge of homogenization in probability, correctors exist for\nall extreme points of the convex hull of the sublevel sets of the effective\nHamiltonian. Even when homogenization is not a priori known, the arguments\nimply existence of correctors and, hence, homogenization in some new settings.\nThese include positively homogeneous Hamiltonians and, hence, geometric-type\nequations including motion by mean curvature, in radially symmetric\nenvironments and for all directions. Correctors also exist and, hence,\nhomogenization holds for many directions for non convex Hamiltoni-ans and\ngeneral stationary ergodic media.\n