Parabolic equations with measurable coefficients

Doyoon Kim; N. V. Krylov

doi:10.1007/s11118-007-9042-8

Parabolic equations with measurable coefficients

Doyoon Kim, N. V. Krylov

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

56 Citations (Scopus)

Abstract

We investigate the unique solvability of second order parabolic equations in non-divergence form in W_p^1,2((0,T) × ℝ^d, p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.

Original language	English
Pages (from-to)	345-361
Number of pages	17
Journal	Potential Analysis
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/s11118-007-9042-8
Publication status	Published - 2007 Jun
Externally published	Yes

Keywords

Second-order equations
Vanishing mean oscillation

ASJC Scopus subject areas

Analysis

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10.1007/s11118-007-9042-8

Cite this

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title = "Parabolic equations with measurable coefficients",

abstract = "We investigate the unique solvability of second order parabolic equations in non-divergence form in Wp1,2((0,T) × ℝd, p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.",

keywords = "Second-order equations, Vanishing mean oscillation",

author = "Doyoon Kim and Krylov, {N. V.}",

note = "Funding Information: The second author was partially supported by NSF Grant DMS-0140405.",

year = "2007",

month = jun,

doi = "10.1007/s11118-007-9042-8",

language = "English",

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pages = "345--361",

journal = "Potential Analysis",

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AU - Kim, Doyoon

AU - Krylov, N. V.

N1 - Funding Information: The second author was partially supported by NSF Grant DMS-0140405.

PY - 2007/6

Y1 - 2007/6

N2 - We investigate the unique solvability of second order parabolic equations in non-divergence form in Wp1,2((0,T) × ℝd, p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.

AB - We investigate the unique solvability of second order parabolic equations in non-divergence form in Wp1,2((0,T) × ℝd, p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.

KW - Second-order equations

KW - Vanishing mean oscillation

UR - http://www.scopus.com/inward/record.url?scp=34247390646&partnerID=8YFLogxK

U2 - 10.1007/s11118-007-9042-8

DO - 10.1007/s11118-007-9042-8

M3 - Article

AN - SCOPUS:34247390646

SN - 0926-2601

VL - 26

SP - 345

EP - 361

JO - Potential Analysis

JF - Potential Analysis

IS - 4

ER -

Parabolic equations with measurable coefficients

Abstract

Keywords

ASJC Scopus subject areas

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