The heat equation in Lq((0, T), Lp)-spaces with weights

N. V. Krylov

doi:10.1137/S0036141000372039

The heat equation in L_q((0, T), L_p)-spaces with weights

N. V. Krylov

School of Mathematics

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

44 Scopus citations

Abstract

Existence and uniqueness theorems are presented for the heat equation in L_p-spaces with or without weights allowing derivatives of solutions to blow up near the boundary. It is allowed for the powers of summability with respect to space and time variables to be different.

Original language	English (US)
Pages (from-to)	1117-1141
Number of pages	25
Journal	SIAM Journal on Mathematical Analysis
Volume	32
Issue number	5
DOIs	https://doi.org/10.1137/S0036141000372039
State	Published - Jan 2001

Keywords

Parabolic equations
Sobolev spaces with weights

Publisher link

10.1137/S0036141000372039

Find It

Find It at U of M Libraries

Cite this

@article{0800ecf0a6cf48d58fed515a68ad486b,

title = "The heat equation in Lq((0, T), Lp)-spaces with weights",

abstract = "Existence and uniqueness theorems are presented for the heat equation in Lp-spaces with or without weights allowing derivatives of solutions to blow up near the boundary. It is allowed for the powers of summability with respect to space and time variables to be different.",

keywords = "Parabolic equations, Sobolev spaces with weights",

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

year = "2001",

month = jan,

doi = "10.1137/S0036141000372039",

language = "English (US)",

volume = "32",

pages = "1117--1141",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

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

number = "5",

}

TY - JOUR

T1 - The heat equation in Lq((0, T), Lp)-spaces with weights

AU - Krylov, N. V.

PY - 2001/1

Y1 - 2001/1

N2 - Existence and uniqueness theorems are presented for the heat equation in Lp-spaces with or without weights allowing derivatives of solutions to blow up near the boundary. It is allowed for the powers of summability with respect to space and time variables to be different.

AB - Existence and uniqueness theorems are presented for the heat equation in Lp-spaces with or without weights allowing derivatives of solutions to blow up near the boundary. It is allowed for the powers of summability with respect to space and time variables to be different.

KW - Parabolic equations

KW - Sobolev spaces with weights

UR - http://www.scopus.com/inward/record.url?scp=0035538198&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035538198&partnerID=8YFLogxK

U2 - 10.1137/S0036141000372039

DO - 10.1137/S0036141000372039

M3 - Article

AN - SCOPUS:0035538198

SN - 0036-1410

VL - 32

SP - 1117

EP - 1141

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 5

ER -