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A regularity theory for quasi-linear Stochastic Partial Differential Equations in weighted Sobolev spaces (1705.01717v1)
Published 4 May 2017 in math.PR
Abstract: We study the second-order quasi-linear stochastic partial differential equations (SPDEs) defined on $C1$ domains. The coefficients are random functions depending on $t,x$ and the unknown solutions. We prove the uniqueness and existence of solutions in appropriate Sobolev spaces, and in addition, we obtain $L_p$ and H\"older estimates of both the solution and its gradient.
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