Hölder regularity of Hamilton-Jacobi equations with stochastic forcing

Cardaliaguet, Pierre; Seeger, Benjamin

doi:10.1090/tran/8435

Hölder regularity of Hamilton-Jacobi equations with stochastic forcing
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by Pierre Cardaliaguet and Benjamin Seeger PDF

Trans. Amer. Math. Soc. 374 (2021), 7197-7233 Request permission

Abstract:

We obtain space-time Hölder regularity estimates for solutions of first- and second-order Hamilton-Jacobi equations perturbed with an additive stochastic forcing term. The bounds depend only on the growth of the Hamiltonian in the gradient and on the regularity of the stochastic coefficients, in a way that is invariant with respect to a hyperbolic scaling.

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