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Journal Articles Calculus of Variations and Partial Differential Equations Year : 2015

Sobolev regularity for the first order Hamilton-Jacobi equation

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 H\"older inequality. Applications to mean field games are discussed.

Dates and versions

hal-01251162 , version 1 (05-01-2016)

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Pierre Cardaliaguet, Alessio Porretta, Daniela Tonon. Sobolev regularity for the first order Hamilton-Jacobi equation. Calculus of Variations and Partial Differential Equations, 2015, 54 (3), pp.3037-3065. ⟨10.1007/s00526-015-0893-3⟩. ⟨hal-01251162⟩
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