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arXiv · 1312.3311

Stochastic De Giorgi Iteration and Regularity of Stochastic Partial Differential Equation

Elton P. Hsu·Yu Wang·Zhenan Wang
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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 H\"older continuous in both space and time variables.

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Elton P. Hsu, Yu Wang, Zhenan Wang. 2013-12-11. Stochastic De Giorgi Iteration and Regularity of Stochastic Partial Differential Equation. https://arxiv.org/abs/1312.3311

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