Advances in Differential Equations

Evolution families and maximal regularity for systems of parabolic equations

Chiara Gallarati and Mark Veraar

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Abstract

In this paper, we prove maximal $L^p$-regularity for a system of parabolic PDEs, where the elliptic operator $A$ has coefficients which depend on time in a measurable way and are continuous in the space variable. The proof is based on operator-theoretic methods and one of the main ingredients in the proof is the construction of an evolution family on weighted $L^q$-spaces.

Article information

Source
Adv. Differential Equations Volume 22, Number 3/4 (2017), 169-190.

Dates
First available in Project Euclid: 18 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1487386866

Subjects
Primary: 42B37: Harmonic analysis and PDE [See also 35-XX] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 34G10: Linear equations [See also 47D06, 47D09] 35B65: Smoothness and regularity of solutions 42B15: Multipliers

Citation

Gallarati, Chiara; Veraar, Mark. Evolution families and maximal regularity for systems of parabolic equations. Adv. Differential Equations 22 (2017), no. 3/4, 169--190.https://projecteuclid.org/euclid.ade/1487386866


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