Stochastic homogenization of a nonconvex Hamilton-Jacobi equation

Scott N. Armstrong (1) , Hung V. Tran (2) , Yifeng Yu (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Department of Mathematics
3 Department of Mathematics

We present a proof of qualitative stochastic homogenization for a nonconvex Hamilton-Jacobi equation. The new idea is to introduce a family of "sub-equations" and to control solutions of the original equation by the maximal subsolutions of the latter, which have deterministic limits by the subadditive ergodic theorem and maximality.

Mots clés: stochastic homogenization; nonconvex Hamilton-Jacobi equation; metric problem

Domaines: Equations aux dérivées partielles [math.AP]

Scott N. Armstrong, Hung V. Tran, Yifeng Yu. Stochastic homogenization of a nonconvex Hamilton-Jacobi equation. Calculus of Variations and Partial Differential Equations, 2015, 54, pp.1507-1524. ⟨10.1007/s00526-015-0833-2⟩. ⟨hal-00903282⟩