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

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  • Kim, Ildoo
  • Kim, Kyeong-Hun

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.

Suggested Citation

  • Kim, Ildoo & Kim, Kyeong-Hun, 2018. "A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 622-643.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:2:p:622-643
    DOI: 10.1016/j.spa.2017.06.006
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    References listed on IDEAS

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    1. Kim, Kyeong-Hun, 2009. "Sobolev space theory of SPDEs with continuous or measurable leading coefficients," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 16-44, January.
    2. Kim, Kyeong-Hun, 2004. "Lq(Lp) theory and Hölder estimates for parabolic SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 313-330, December.
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