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arXiv · 1510.07643

Evolution families and maximal regularity for systems of parabolic equations

Chiara Gallarati·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.

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Chiara Gallarati, Mark Veraar. 2015-10-26. Evolution families and maximal regularity for systems of parabolic equations. https://arxiv.org/abs/1510.07643

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