Hölder regularity for a non-linear parabolic equation driven by space-time white noise
Félix Otto, Hendrik Weber · arXiv (Cornell University) · 2015
We consider the non-linear equation $T^{-1} u+\partial_tu-\partial_x^2π(u)=ξ$ driven by space-time white noise $ξ$, which is uniformly parabolic because we assume that $π'$ is bounded away from zero and infinity. Under the further assumption of Lipschitz continuity of $π'$ we show that the stationary solution is - as for the linear case - almost surely Hölder continuous with exponent $α$ for any $α