A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces

Ildoo Kim and Kyeong-Hun Kim

Stochastic Processes and their Applications, 2018, vol. 128, issue 2, 622-643

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 Lp and Hölder estimates of both the solution and its gradient.

Keywords: Nonlinear stochastic partial differential equations; Equations of divergence type; Weighted Sobolev space (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:2:p:622-643

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DOI: 10.1016/j.spa.2017.06.006

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