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Hölder regularity of Hamilton-Jacobi equations with stochastic forcing

Cardaliaguet, Pierre; Seeger, Benjamin (2021), Hölder regularity of Hamilton-Jacobi equations with stochastic forcing, Transactions of the American Mathematical Society, 374, p. 7197-7233. 10.1090/tran/8435

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Transactions of the American Mathematical Society
Volume
374
Publisher
American Mathematical Society
Pages
7197-7233
Publication identifier
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Author(s)
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Seeger, Benjamin
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
Hamilton-Jacobi equations; stochastic PDEs; Hölder regularity