Hyperbolicity of minimizers and regularity of viscosity solutions for random Hamilton-Jacobi equations

2012/01/16 by Konstantin Khanin, Ke Zhang, Khanin, Konstantin +1 · 1 citation
Mathematics · Physics and Astronomy · #34F05 #37D25 #70H20 #76F20 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.DS #msc:34F05 #msc:37D25 #msc:70H20 #msc:76F20

paper · pdf · doi:10.48550/arxiv.1201.3381

Updated version March 2017

openalex publication_date 2012/01/16 · arxiv created 2017/03/29 · arxiv updated 2017/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for a family of randomly kicked Hamilton-Jacobi equations, the unique global minimizer is hyperbolic, almost surely. Furthermore, we prove the unique forward and backward viscosity solutions, though in general only Lipshitz, are smooth in a neighbourhood of the global minimizer. Our result generalizes the result of E, Khanin, Mazel and Sinai (\citeEKMS00) to dimension d≥ 2, and extends the result of Iturriaga and Khanin in \citeIK03.

Citations

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