Work

Sobolev regularity for the first order Hamilton-Jacobi equation

Year: 2014

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1411.0227

Authors: Cardaliaguet, Pierre, Porretta, Alessio, Tonon, Daniela

Institutions: Centre de Recherche en Mathématiques de la Décision, Université Paris Dauphine-PSL, University of Rome Tor Vergata

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: G6702880738, Hamilton-Jacobi equations on heterogeneous structures and networks