A Sobolev space theory of SPDEs with constant coefficients in a half space

N. V. Krylov; S. V. Lototsky

doi:10.1137/S0036141098338843

A Sobolev space theory of SPDEs with constant coefficients in a half space

N. V. Krylov, S. V. Lototsky

School of Mathematics

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

61 Scopus citations

Abstract

Equations of the form du = (a^{Script i signScript j sign}Script u sign_{cursive greek chiScript i signcursive greek chiScript j sign} + D_{Script i sign}Script f sign^{Script i sign}) Script d signScript t sign + Σ_{Script k sign}(σ^{Script i signScript k sign}Script u sign_{cursive greek chiScript i sign} + Script g sign^{Script k sign})Script d signScript w sign^{Script k sign}_{Script t sign} are considered for Script t sign > 0 and cursive greek chi ∈ ℝ^{Script d sign}₊. The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power Script p sign ∈ (2, ∞).

Original language	English (US)
Pages (from-to)	19-33
Number of pages	15
Journal	SIAM Journal on Mathematical Analysis
Volume	31
Issue number	1
DOIs	https://doi.org/10.1137/S0036141098338843
State	Published - 1999

Keywords

Sobolev spaces with weights
Stochastic partial differential equations

Publisher link

10.1137/S0036141098338843

Find It

Find It at U of M Libraries

Cite this

@article{4997c64b77b84e7884f2365d63c68c8c,

title = "A Sobolev space theory of SPDEs with constant coefficients in a half space",

abstract = "Equations of the form du = (aScript i signScript j signScript u signcursive greek chiScript i signcursive greek chiScript j sign + DScript i signScript f signScript i sign) Script d signScript t sign + ΣScript k sign(σScript i signScript k signScript u signcursive greek chiScript i sign + Script g signScript k sign)Script d signScript w signScript k signScript t sign are considered for Script t sign > 0 and cursive greek chi ∈ ℝScript d sign+. The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power Script p sign ∈ (2, ∞).",

keywords = "Sobolev spaces with weights, Stochastic partial differential equations",

author = "Krylov, {N. V.} and Lototsky, {S. V.}",

year = "1999",

doi = "10.1137/S0036141098338843",

language = "English (US)",

volume = "31",

pages = "19--33",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - A Sobolev space theory of SPDEs with constant coefficients in a half space

AU - Krylov, N. V.

AU - Lototsky, S. V.

PY - 1999

Y1 - 1999

N2 - Equations of the form du = (aScript i signScript j signScript u signcursive greek chiScript i signcursive greek chiScript j sign + DScript i signScript f signScript i sign) Script d signScript t sign + ΣScript k sign(σScript i signScript k signScript u signcursive greek chiScript i sign + Script g signScript k sign)Script d signScript w signScript k signScript t sign are considered for Script t sign > 0 and cursive greek chi ∈ ℝScript d sign+. The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power Script p sign ∈ (2, ∞).

AB - Equations of the form du = (aScript i signScript j signScript u signcursive greek chiScript i signcursive greek chiScript j sign + DScript i signScript f signScript i sign) Script d signScript t sign + ΣScript k sign(σScript i signScript k signScript u signcursive greek chiScript i sign + Script g signScript k sign)Script d signScript w signScript k signScript t sign are considered for Script t sign > 0 and cursive greek chi ∈ ℝScript d sign+. The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power Script p sign ∈ (2, ∞).

KW - Sobolev spaces with weights

KW - Stochastic partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=0033233494&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033233494&partnerID=8YFLogxK

U2 - 10.1137/S0036141098338843

DO - 10.1137/S0036141098338843

M3 - Article

AN - SCOPUS:0033233494

SN - 0036-1410

VL - 31

SP - 19

EP - 33

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

A Sobolev space theory of SPDEs with constant coefficients in a half space

Abstract

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this