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Local Regularity for Fractional Heat Equations

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Recent Advances in PDEs: Analysis, Numerics and Control

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 17))

Abstract

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set \(\Omega \subset {\mathbb {R}}^N\). Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.

Dedicated to Prof. Enrique Fernández-Cara on the occasion of his 60th birthday.

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Acknowledgments

The work of Umberto Biccari was partially supported by the Advanced Grant DYCON (Dynamic Control) of the European Research Council Executive Agency, by the MTM2014-52347 and MTM2017-92996 Grants of the MINECO (Spain) and by the Air Force Office of Scientific Research under the Award No: FA9550-15-1-0027. The work of Mahamadi Warma was partially supported by the Air Force Office of Scientific Research under the Award No: FA9550-15-1-0027. The work of Enrique Zuazua was partially supported by the Advanced Grant DYCON (Dynamic Control) of the European Research Council Executive Agency, FA9550-15-1-0027 of AFOSR, FA9550-14-1-0214 of the EOARD-AFOSR, the MTM2014-52347 and MTM2017-92996 Grants of the MINECO (Spain) and ICON of the French ANR

Author information

Authors and Affiliations

  1. DeustoTech, University of Deusto, Bilbao, Basque Country, Spain

    Umberto Biccari & Enrique Zuazua

  2. Facultad de Ingeniería, Universidad de Deusto, Bilbao, Basque Country, Spain

    Umberto Biccari & Enrique Zuazua

  3. University of Puerto Rico (Rio Piedras Campus), College of Natural Sciences, Department of Mathematics, San Juan, PR, USA

    Mahamadi Warma

  4. Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain

    Enrique Zuazua

  5. Sorbonne Universites, UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France

    Enrique Zuazua

Authors
  1. Umberto Biccari
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  2. Mahamadi Warma
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  3. Enrique Zuazua
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Corresponding author

Correspondence to Enrique Zuazua .

Editor information

Editors and Affiliations

  1. Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain

    Anna Doubova

  2. Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain

    Manuel González-Burgos

  3. Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain

    Francisco Guillén-González

  4. Departamento de Informática y Análisis Numérico, Universidad de Córdoba, Córdoba, Spain

    Mercedes Marín Beltrán

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Biccari, U., Warma, M., Zuazua, E. (2018). Local Regularity for Fractional Heat Equations. In: Doubova, A., González-Burgos, M., Guillén-González, F., Marín Beltrán, M. (eds) Recent Advances in PDEs: Analysis, Numerics and Control. SEMA SIMAI Springer Series, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-97613-6_12

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