Hölder regularity of Hamilton-Jacobi equations with stochastic forcing

Hölder regularity of Hamilton-Jacobi equations with stochastic forcing

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 w...

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Veröffentlicht in:Transactions of the American Mathematical Society 2021-10, Vol.374 (10), p.7197-7233
Hauptverfasser: Cardaliaguet, Pierre, Seeger, Benjamin
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Mathematics
Research article
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Zusammenfassung: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8435