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 Holder inequality. Applications to mean field games are discussed.

Cardaliaguet, P., Porretta, A., Tonon, D. (2015). Sobolev regularity for the first order Hamilton–Jacobi equation. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 54(3), 3037-3065 [10.1007/s00526-015-0893-3].

Sobolev regularity for the first order Hamilton–Jacobi equation

PORRETTA, ALESSIO;
2015

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 Holder inequality. Applications to mean field games are discussed.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
Cardaliaguet, P., Porretta, A., Tonon, D. (2015). Sobolev regularity for the first order Hamilton–Jacobi equation. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 54(3), 3037-3065 [10.1007/s00526-015-0893-3].
Cardaliaguet, P; Porretta, A; Tonon, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/172889
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