Stochastic De Giorgi Iteration and Regularity of Stochastic Partial Differential Equation

Abstract

Under general conditions we show that the solution of a stochastic parabolic partial differential equation of the form \[ \partial_t u = \mathrm{div} (A \nabla u) + f(t,x, u) + g_i (t,x,u) \dot{w}^i_t \] is almost surely Hölder continuous in both space and time variables.

Cited by in corpus (3)

• Local $L_{\infty }$-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs
• Regularity of stochastic nonlocal diffusion equations
• Morrey-Campanato estimates for the moments of stochastic integral operators and its application to SPDEs