Sobolev regularity for the first order Hamilton-Jacobi equation

2014/11/02 by Pierre Cardaliaguet, Cardaliaguet, Pierre, Alessio Porretta +3
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Stochastic processes and financial applications #math.AP

paper · pdf · doi:10.48550/arxiv.1411.0227

arxiv created 2014/11/02 · openalex publication_date 2014/11/02 · arxiv updated 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide Sobolev estimates for solutions of first order Hamilton-Jacobi equations with Hamiltonians which are superlinear in the gradient variable. We also show that the solutions are differentiable almost everywhere. The proof relies on an inverse Hölder inequality. Applications to mean field games are discussed.

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