A regularity theory for quasi-linear stochastic partial differential equations in weighted Sobolev spaces

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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.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2017 May 4

Keywords

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

ASJC Scopus subject areas

  • General

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