Advances in Differential Equations

Evolution families and maximal regularity for systems of parabolic equations

Chiara Gallarati and Mark Veraar

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 18 February 2017

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation