Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations

Matthias Georg Hieber, Sylvie Monniaux

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In this paper, we show that a pseudo-differential operator associated to a symbol a ε L(ℝ × ℝ, L(H)) (H being a Hubert space) which admits a holomorphic extension to a suitable sector of ℂ acts as a bounded operator on L2(ℝ, H). By showing that maximal Lp-regularity for the nonautonomous parabolic equation u′(t)+A(t)u(t) = f(t), u(0) = 0 is independent of p ε (1, ∞), we obtain as a consequence a maximal Lp([0, T], H)-regularity result for solutions of the above equation.

Original languageEnglish
Pages (from-to)1047-1053
Number of pages7
JournalProceedings of the American Mathematical Society
Volume128
Issue number4
Publication statusPublished - 2000
Externally publishedYes

Fingerprint

Maximal Regularity
Nonautonomous Equation
Pseudodifferential Operators
Parabolic Equation
Regularity
Holomorphic Extension
Hubert Space
Bounded Operator
Sector

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations. / Hieber, Matthias Georg; Monniaux, Sylvie.

In: Proceedings of the American Mathematical Society, Vol. 128, No. 4, 2000, p. 1047-1053.

Research output: Contribution to journalArticle

@article{34cff70778eb4acd9051a735c96b2e4a,
title = "Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations",
abstract = "In this paper, we show that a pseudo-differential operator associated to a symbol a ε L∞(ℝ × ℝ, L(H)) (H being a Hubert space) which admits a holomorphic extension to a suitable sector of ℂ acts as a bounded operator on L2(ℝ, H). By showing that maximal Lp-regularity for the nonautonomous parabolic equation u′(t)+A(t)u(t) = f(t), u(0) = 0 is independent of p ε (1, ∞), we obtain as a consequence a maximal Lp([0, T], H)-regularity result for solutions of the above equation.",
author = "Hieber, {Matthias Georg} and Sylvie Monniaux",
year = "2000",
language = "English",
volume = "128",
pages = "1047--1053",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "4",

}

TY - JOUR

T1 - Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations

AU - Hieber, Matthias Georg

AU - Monniaux, Sylvie

PY - 2000

Y1 - 2000

N2 - In this paper, we show that a pseudo-differential operator associated to a symbol a ε L∞(ℝ × ℝ, L(H)) (H being a Hubert space) which admits a holomorphic extension to a suitable sector of ℂ acts as a bounded operator on L2(ℝ, H). By showing that maximal Lp-regularity for the nonautonomous parabolic equation u′(t)+A(t)u(t) = f(t), u(0) = 0 is independent of p ε (1, ∞), we obtain as a consequence a maximal Lp([0, T], H)-regularity result for solutions of the above equation.

AB - In this paper, we show that a pseudo-differential operator associated to a symbol a ε L∞(ℝ × ℝ, L(H)) (H being a Hubert space) which admits a holomorphic extension to a suitable sector of ℂ acts as a bounded operator on L2(ℝ, H). By showing that maximal Lp-regularity for the nonautonomous parabolic equation u′(t)+A(t)u(t) = f(t), u(0) = 0 is independent of p ε (1, ∞), we obtain as a consequence a maximal Lp([0, T], H)-regularity result for solutions of the above equation.

UR - http://www.scopus.com/inward/record.url?scp=23044520222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044520222&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23044520222

VL - 128

SP - 1047

EP - 1053

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -