A regularity theory for quasi-linear Stochastic Partial Differential Equations in weighted Sobolev spaces

2017/05/04 by Kim, Ildoo, Kim, Kyeong-hun
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1705.01717

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 Hölder estimates of both the solution and its gradient.

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