Parabolic equations with partially BMO coefficients and boundary value problems in Sobolev spaces with mixed norms

Doyoon Kim

doi:10.1007/s11118-009-9158-0

Parabolic equations with partially BMO coefficients and boundary value problems in Sobolev spaces with mixed norms

Doyoon Kim

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

16 Citations (Scopus)

Abstract

Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a¹¹) are measurable in time and one spatial variable, and have small BMO (bounded mean oscillation) semi-norms as functions of the other spatial variables. The coefficient a¹¹ is measurable in time and have a small BMO semi-norm in the spatial variables. The unique solvability of equations in the whole space is established. Then this result is applied to solving Dirichlet and Neumann boundary value problems for parabolic equations defined on a half-space or on a bounded domain.

Original language	English
Pages (from-to)	17-46
Number of pages	30
Journal	Potential Analysis
Volume	33
Issue number	1
DOIs	https://doi.org/10.1007/s11118-009-9158-0
Publication status	Published - 2010
Externally published	Yes

Keywords

Bounded mean oscillation
Dirichlet and Neumann boundary value problems
Second order parabolic equations
Sobolev spaces with mixed norms

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/s11118-009-9158-0

Fingerprint Dive into the research topics of 'Parabolic equations with partially BMO coefficients and boundary value problems in Sobolev spaces with mixed norms'. Together they form a unique fingerprint.

Cite this

@article{1403b4b83a2c4d49bed4e43ca5d7cca1,

title = "Parabolic equations with partially BMO coefficients and boundary value problems in Sobolev spaces with mixed norms",

abstract = "Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a11) are measurable in time and one spatial variable, and have small BMO (bounded mean oscillation) semi-norms as functions of the other spatial variables. The coefficient a11 is measurable in time and have a small BMO semi-norm in the spatial variables. The unique solvability of equations in the whole space is established. Then this result is applied to solving Dirichlet and Neumann boundary value problems for parabolic equations defined on a half-space or on a bounded domain.",

keywords = "Bounded mean oscillation, Dirichlet and Neumann boundary value problems, Second order parabolic equations, Sobolev spaces with mixed norms",

author = "Doyoon Kim",

year = "2010",

doi = "10.1007/s11118-009-9158-0",

language = "English",

volume = "33",

pages = "17--46",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Parabolic equations with partially BMO coefficients and boundary value problems in Sobolev spaces with mixed norms

AU - Kim, Doyoon

PY - 2010

Y1 - 2010

N2 - Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a11) are measurable in time and one spatial variable, and have small BMO (bounded mean oscillation) semi-norms as functions of the other spatial variables. The coefficient a11 is measurable in time and have a small BMO semi-norm in the spatial variables. The unique solvability of equations in the whole space is established. Then this result is applied to solving Dirichlet and Neumann boundary value problems for parabolic equations defined on a half-space or on a bounded domain.

AB - Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a11) are measurable in time and one spatial variable, and have small BMO (bounded mean oscillation) semi-norms as functions of the other spatial variables. The coefficient a11 is measurable in time and have a small BMO semi-norm in the spatial variables. The unique solvability of equations in the whole space is established. Then this result is applied to solving Dirichlet and Neumann boundary value problems for parabolic equations defined on a half-space or on a bounded domain.

KW - Bounded mean oscillation

KW - Dirichlet and Neumann boundary value problems

KW - Second order parabolic equations

KW - Sobolev spaces with mixed norms

UR - http://www.scopus.com/inward/record.url?scp=74449089766&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74449089766&partnerID=8YFLogxK

U2 - 10.1007/s11118-009-9158-0

DO - 10.1007/s11118-009-9158-0

M3 - Article

AN - SCOPUS:74449089766

VL - 33

SP - 17

EP - 46

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

IS - 1

ER -

Parabolic equations with partially BMO coefficients and boundary value problems in Sobolev spaces with mixed norms

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this