Jialin Hong, Chuying Huang, Zhihui Liu
Published 2017-09-25Version 1
In this paper, we prove the well-posedness and op- timal trajectory regularity for the solution of stochastic evolution equations driven by general multiplicative noises in martingale type 2 Banach spaces. The main idea of our method is to combine the approach in [HL] dealing with Hilbert setting and a version of Burkholder inequality in M-type 2 Banach space. Applying our main results to the stochastic heat equation gives a positive an- swer to an open problem proposed in [JR12].
An $L_p$-estimate for the stochastic heat equation on an angular domain in $\mathbb{R}^2$
Singular Behavior of the Solution to the Stochastic Heat Equation on a Polygonal Domain
On the spatial dynamics of the solution to the stochastic heat equation
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