Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms

N. V. Krylov

doi:10.1016/j.jfa.2007.04.003

Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms

N. V. Krylov

School of Mathematics

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

89 Scopus citations

Abstract

An L_q (L_p)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class VMO_x, which, in particular, contains all measurable functions depending only on t. The method of proving simplifies the methods previously used in the case p = q.

Original language	English (US)
Pages (from-to)	521-558
Number of pages	38
Journal	Journal of Functional Analysis
Volume	250
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2007.04.003
State	Published - Sep 15 2007

Bibliographical note

Funding Information:
✩ The work was partially supported by NSF Grants DMS-0140405 and DMS-0653121. E-mail address: [email protected].

Keywords

Mixed norms
Second-order equations
Vanishing mean oscillation

Publisher link

10.1016/j.jfa.2007.04.003

Find It

Find It at U of M Libraries

Cite this

@article{9e693ef2c61349ad9c19a0b1f361b890,

title = "Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms",

abstract = "An Lq (Lp)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class VMOx, which, in particular, contains all measurable functions depending only on t. The method of proving simplifies the methods previously used in the case p = q.",

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

author = "Krylov, {N. V.}",

note = "Funding Information: ✩ The work was partially supported by NSF Grants DMS-0140405 and DMS-0653121. E-mail address: [email protected].",

year = "2007",

month = sep,

day = "15",

doi = "10.1016/j.jfa.2007.04.003",

language = "English (US)",

volume = "250",

pages = "521--558",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms

AU - Krylov, N. V.

N1 - Funding Information: ✩ The work was partially supported by NSF Grants DMS-0140405 and DMS-0653121. E-mail address: [email protected].

PY - 2007/9/15

Y1 - 2007/9/15

N2 - An Lq (Lp)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class VMOx, which, in particular, contains all measurable functions depending only on t. The method of proving simplifies the methods previously used in the case p = q.

AB - An Lq (Lp)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class VMOx, which, in particular, contains all measurable functions depending only on t. The method of proving simplifies the methods previously used in the case p = q.

KW - Mixed norms

KW - Second-order equations

KW - Vanishing mean oscillation

UR - http://www.scopus.com/inward/record.url?scp=34547701915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547701915&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2007.04.003

DO - 10.1016/j.jfa.2007.04.003

M3 - Article

AN - SCOPUS:34547701915

SN - 0022-1236

VL - 250

SP - 521

EP - 558

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this