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

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3 Citations (Scopus)

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
JournalStochastic Processes and their Applications
DOIs
Publication statusAccepted/In press - 2017

Keywords

  • 35R60
  • 60H15
  • 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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