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

Research output: Contribution to journalArticle

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

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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

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title = "A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces",
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 H{\"o}lder estimates of both the solution and its gradient.",
keywords = "35R60, 60H15, Equations of divergence type, Nonlinear stochastic partial differential equations, Weighted Sobolev space",
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language = "English",
journal = "Stochastic Processes and their Applications",
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AU - Kim, Kyeong Hun

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AB - 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.

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KW - Equations of divergence type

KW - Nonlinear stochastic partial differential equations

KW - Weighted Sobolev space

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