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

Ildoo Kim, Kyeong Hun Kim

Research output: Contribution to journal › Article

1 Citation (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

Fingerprint

Stochastic PDEs
Regularity Theory
Sobolev spaces
Weighted Sobolev Spaces
Stochastic Partial Differential Equations
Random Function
Linear partial differential equation
Existence and Uniqueness of Solutions
Sobolev Spaces
Gradient
Unknown
Coefficient
Estimate
Partial differential equations

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

Cite this

A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces. / Kim, Ildoo; Kim, Kyeong Hun.

In: Stochastic Processes and their Applications, 2017.

Research output: Contribution to journal › Article

Kim, I & Kim, KH 2017, 'A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces', Stochastic Processes and their Applications. https://doi.org/10.1016/j.spa.2017.06.006
Kim I, Kim KH. A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces. Stochastic Processes and their Applications. 2017. https://doi.org/10.1016/j.spa.2017.06.006
Kim, Ildoo ; Kim, Kyeong Hun. / A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces. In: Stochastic Processes and their Applications. 2017.
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