Advances in Differential Equations

Maximal regularity and kernel bounds: observations on a theorem by Hieber and Prüss

Thierry Coulhon and Xuan Thinh Duong

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Abstract

For $1 <p,q <+\infty$, we show the maximal $L^q$ regularity for the inhomogeneous evolution equation in $L^p(\Omega)$ associated with the infinitesimal generator of a semigroup whose kernel satisfies suitable upper bounds, with $\Omega$ a subset of a space of homogeneous type.

Article information

Source
Adv. Differential Equations Volume 5, Number 1-3 (2000), 343-368.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651388

Mathematical Reviews number (MathSciNet)
MR1734546

Zentralblatt MATH identifier
1001.34046

Subjects
Primary: 34G10: Linear equations [See also 47D06, 47D09]
Secondary: 35K90: Abstract parabolic equations 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]

Citation

Coulhon, Thierry; Duong, Xuan Thinh. Maximal regularity and kernel bounds: observations on a theorem by Hieber and Prüss. Adv. Differential Equations 5 (2000), no. 1-3, 343--368. https://projecteuclid.org/euclid.ade/1356651388.


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