Sobolev space theory of SPDEs with continuous or measurable leading coefficients

Kyeong Hun Kim

doi:10.1016/j.spa.2008.01.009

Sobolev space theory of SPDEs with continuous or measurable leading coefficients

Kyeong Hun Kim^*

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

We study stochastic partial differential equations with variable coefficients defined on R^d, R₊^d and bounded C¹ domains. For equations with continuous leading coefficients we give existence and uniqueness results in L_q (L_p)-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different. For equations with measurable leading coefficients we give unique solvability in L_p-spaces.

Original language	English
Pages (from-to)	16-44
Number of pages	29
Journal	Stochastic Processes and their Applications
Volume	119
Issue number	1
DOIs	https://doi.org/10.1016/j.spa.2008.01.009
Publication status	Published - 2009 Jan

Bibliographical note

Funding Information:
This work was supported by the Korean Research Foundation Grant funded by the Korean Government KRF-2007-313-C00072.

Keywords

L (L)-theory
L-theory
Measurable coefficients
Sobolev spaces with weights
Stochastic partial differential equations

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/j.spa.2008.01.009

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title = "Sobolev space theory of SPDEs with continuous or measurable leading coefficients",

abstract = "We study stochastic partial differential equations with variable coefficients defined on Rd, R+d and bounded C1 domains. For equations with continuous leading coefficients we give existence and uniqueness results in Lq (Lp)-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different. For equations with measurable leading coefficients we give unique solvability in Lp-spaces.",

keywords = "L (L)-theory, L-theory, Measurable coefficients, Sobolev spaces with weights, Stochastic partial differential equations",

author = "Kim, \{Kyeong Hun\}",

note = "Funding Information: This work was supported by the Korean Research Foundation Grant funded by the Korean Government KRF-2007-313-C00072.",

year = "2009",

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doi = "10.1016/j.spa.2008.01.009",

language = "English",

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AU - Kim, Kyeong Hun

N1 - Funding Information: This work was supported by the Korean Research Foundation Grant funded by the Korean Government KRF-2007-313-C00072.

PY - 2009/1

Y1 - 2009/1

N2 - We study stochastic partial differential equations with variable coefficients defined on Rd, R+d and bounded C1 domains. For equations with continuous leading coefficients we give existence and uniqueness results in Lq (Lp)-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different. For equations with measurable leading coefficients we give unique solvability in Lp-spaces.

AB - We study stochastic partial differential equations with variable coefficients defined on Rd, R+d and bounded C1 domains. For equations with continuous leading coefficients we give existence and uniqueness results in Lq (Lp)-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different. For equations with measurable leading coefficients we give unique solvability in Lp-spaces.

KW - L (L)-theory

KW - L-theory

KW - Measurable coefficients

KW - Sobolev spaces with weights

KW - Stochastic partial differential equations

UR - https://www.scopus.com/pages/publications/57149100814

U2 - 10.1016/j.spa.2008.01.009

DO - 10.1016/j.spa.2008.01.009

M3 - Article

AN - SCOPUS:57149100814

SN - 0304-4149

VL - 119

SP - 16

EP - 44

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Sobolev space theory of SPDEs with continuous or measurable leading coefficients

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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