Heat-Kernels and Maximal LP-Lq-Estimates: The Non-Autonomous Case

Matthias Georg Hieber; Sylvie Monniaux

Heat-Kernels and Maximal LP-Lq-Estimates: The Non-Autonomous Case

Matthias Georg Hieber^*, Sylvie Monniaux

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

In this paper, we establish maximal L^p-L^q estimates for non-autonomous parabolic equations of the type u′(t) + A(t)u(t) = f(t), u(0) = 0 under suitable conditions on the kernels of the semigroups generated by the operators -A(t), t ∈ [0, T]. We apply this result on semilinear problems of the form u′(t) + A(t)u(t) = f(t, u(t)), u(0) = 0.

Original language	English
Pages (from-to)	467-481
Number of pages	15
Journal	Journal of Knot Theory and its Ramifications
Volume	6
Issue number	5
Publication status	Published - 2000
Externally published	Yes

Keywords

Heat-kernel estimates
Maximal l - L-regularity
Non-autonomous cauchy problem
Singular integrals

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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title = "Heat-Kernels and Maximal LP-Lq-Estimates: The Non-Autonomous Case",

abstract = "In this paper, we establish maximal Lp-Lq estimates for non-autonomous parabolic equations of the type u′(t) + A(t)u(t) = f(t), u(0) = 0 under suitable conditions on the kernels of the semigroups generated by the operators -A(t), t ∈ [0, T]. We apply this result on semilinear problems of the form u′(t) + A(t)u(t) = f(t, u(t)), u(0) = 0.",

keywords = "Heat-kernel estimates, Maximal l - L-regularity, Non-autonomous cauchy problem, Singular integrals",

author = "Hieber, {Matthias Georg} and Sylvie Monniaux",

year = "2000",

language = "English",

volume = "6",

pages = "467--481",

journal = "Journal of Knot Theory and its Ramifications",

issn = "0218-2165",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "5",

}

TY - JOUR

T1 - Heat-Kernels and Maximal LP-Lq-Estimates

T2 - The Non-Autonomous Case

AU - Hieber, Matthias Georg

AU - Monniaux, Sylvie

PY - 2000

Y1 - 2000

N2 - In this paper, we establish maximal Lp-Lq estimates for non-autonomous parabolic equations of the type u′(t) + A(t)u(t) = f(t), u(0) = 0 under suitable conditions on the kernels of the semigroups generated by the operators -A(t), t ∈ [0, T]. We apply this result on semilinear problems of the form u′(t) + A(t)u(t) = f(t, u(t)), u(0) = 0.

AB - In this paper, we establish maximal Lp-Lq estimates for non-autonomous parabolic equations of the type u′(t) + A(t)u(t) = f(t), u(0) = 0 under suitable conditions on the kernels of the semigroups generated by the operators -A(t), t ∈ [0, T]. We apply this result on semilinear problems of the form u′(t) + A(t)u(t) = f(t, u(t)), u(0) = 0.

KW - Heat-kernel estimates

KW - Maximal l - L-regularity

KW - Non-autonomous cauchy problem

KW - Singular integrals

UR - http://www.scopus.com/inward/record.url?scp=0346056028&partnerID=8YFLogxK

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M3 - Article

AN - SCOPUS:0346056028

SN - 0218-2165

VL - 6

SP - 467

EP - 481

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 5

ER -

Heat-Kernels and Maximal LP-Lq-Estimates: The Non-Autonomous Case

Abstract

Keywords

ASJC Scopus subject areas

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