New maximal regularity results for the heat equation in exterior domains, and applications

Details New maximal regularity results for the heat equation in exterior domains, and applications New maximal regularity results for the heat equation in exterior domains, and applications

2012-03-06

arxiv.org/abs/1203.1129v1

Mathematics

Analysis of PDEs

28 pages

Scientific paper

This paper is dedicated to the proof of new maximal regularity results involving Besov spaces for the heat equation in the half-space or in bounded or exterior domains of R^n. We strive for time independent a priori estimates in regularity spaces of type L^1(0,T;X) where X stands for some homogeneous Besov space. In the case of bounded domains, the results that we get are similar to those of the whole space or of the half-space. For exterior domains, we need to use mixed Besov norms in order to get a control on the low frequencies. Those estimates are crucial for proving global-in-time results for nonlinear heat equations in a critical functional framework.

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