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

Ildoo Kim; Kyeong Hun Kim

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

Department of Mathematics

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

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 L_p and Hölder estimates of both the solution and its gradient.

Original language	English
Journal	Unknown Journal
Publication status	Published - 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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title = "A regularity theory for quasi-linear stochastic partial differential equations 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.",

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author = "Ildoo Kim and Kim, {Kyeong Hun}",

year = "2017",

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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 - Equations of divergence type

KW - Quasilinear stochastic partial differential equations

KW - Weighted Sobolev space

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