Regularization by noise for stochastic Hamilton-Jacobi equations

2016/09/22 by Gassiat, Paul, Gess, Benjamin · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1609.07074

Abstract

We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE. More precisely, path-by-path L^∞ bounds for the second derivative of solutions to such PDE are shown. These bounds are expressed as solutions to reflected SDE and are shown to be optimal.

Cited by

• Local pathwise solutions and regularization by noises for the stochastic hyperbolic Keller-Segel equation

Related

• Hölder regularity of Hamilton-Jacobi equations with stochastic forcing
• New regularity results and long time behavior of pathwise (stochastic) Hamilton-Jacobi equations
• Long-time behaviour of stochastic Hamilton-Jacobi equations
• Stochastic PDEs with Generalized Coercivity: Global Well-Posedness and Finite Time Extinction
• Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications