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

Ildoo Kim; Kyeong Hun Kim

doi:10.1016/j.spa.2017.06.006

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

Ildoo Kim, Kyeong Hun Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Journal	Stochastic Processes and their Applications
DOIs	https://doi.org/10.1016/j.spa.2017.06.006
Publication status	Accepted/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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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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T1 - A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces

AU - Kim, Ildoo

AU - Kim, Kyeong Hun

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N2 - 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.

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.

KW - 35R60

KW - 60H15

KW - Equations of divergence type

KW - Nonlinear stochastic partial differential equations

KW - Weighted Sobolev space

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DO - 10.1016/j.spa.2017.06.006

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JF - Stochastic Processes and their Applications

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