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;
2015-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
