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

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

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

Original language	English
Pages (from-to)	622-643
Number of pages	22
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	2
DOIs	https://doi.org/10.1016/j.spa.2017.06.006
Publication status	Published - 2018 Feb

Bibliographical note

Funding Information:
The research of the first author was supported by the TJ Park Science Fellowship of POSCO TJ Park Foundation . The research of the second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 20120005158 ).

Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

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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10.1016/j.spa.2017.06.006

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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 = "Equations of divergence type, Nonlinear stochastic partial differential equations, Weighted Sobolev space",

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

note = "Funding Information: The research of the first author was supported by the TJ Park Science Fellowship of POSCO TJ Park Foundation . The research of the second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 20120005158 ). Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

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AU - Kim, Ildoo

AU - Kim, Kyeong Hun

N1 - Funding Information: The research of the first author was supported by the TJ Park Science Fellowship of POSCO TJ Park Foundation . The research of the second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 20120005158 ). Publisher Copyright: © 2017 Elsevier B.V.

PY - 2018/2

Y1 - 2018/2

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 - Nonlinear stochastic partial differential equations

KW - Weighted Sobolev space

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U2 - 10.1016/j.spa.2017.06.006

DO - 10.1016/j.spa.2017.06.006

M3 - Article

AN - SCOPUS:85023625298

SN - 0304-4149

VL - 128

SP - 622

EP - 643

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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