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

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6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)622-643
Number of pages22
JournalStochastic Processes and their Applications
Issue number2
Publication statusPublished - 2018 Feb

Bibliographical note

Funding Information:
The research of the first author was supported by the TJ Park Science Fellowship of POSCO TJ Park Foundation . The research of the second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 20120005158 ).

Publisher Copyright:
© 2017 Elsevier B.V.


  • Equations of divergence type
  • Nonlinear stochastic partial differential equations
  • Weighted Sobolev space

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics


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