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Sobolev regularity for the first order Hamilton–Jacobi equation

Cardaliaguet, Pierre; Porretta, Alessio; Tonon, Daniela (2015), Sobolev regularity for the first order Hamilton–Jacobi equation, Calculus of Variations and Partial Differential Equations, 54, 3, p. 3037-3065. 10.1007/s00526-015-0893-3

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1411.0227v1
Date
2015
Journal name
Calculus of Variations and Partial Differential Equations
Volume
54
Number
3
Publisher
Springer
Pages
3037-3065
Publication identifier
Metadata
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Author(s)
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Porretta, Alessio
Dipartimento di Matematica [Rome]
Tonon, Daniela
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We provide Sobolev estimates for solutions of first order Hamilton-Jacobi equa-tions with Hamiltonians which are superlinear in the gradient variable. We also show that thesolutions are differentiable almost everywhere. The proof relies on an inverse H ̈older inequality.Applications to mean field games are discussed.
Subjects / Keywords
Reverse Hölder inequality; Mean Field Games; Hamilton-Jacobi equation