New Maximal Regularity Results for the Heat Equation in Exterior Domains, and Applications

Chapter
First Online:
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 84)

Abstract

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.

Key words

Besov spaces Exterior domain Heat equation Maximal regularity L1 regularity 
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Notes

Acknowledgements

The second author has been supported by the MN grant IdP2011 000661.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.LAMA, UMR 8050Université Paris-Est et Institut Universitaire de FranceCréteil CedexFrance
  2. 2.Instytut Matematyki Stosowanej i MechanikiUniwersytet WarszawskiWarszawaPoland

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