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Nonlocal
self-improving properties: a functional analytic approach
Pascal Auscher, Simon Bortz, Moritz Egert and Olli Saari |
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Vol. 1 (2019), No. 2, 151–183
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Abstract |
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A functional analytic approach to obtaining self-improving properties of solutions to linear nonlocal elliptic equations is presented. It yields conceptually simple and very short proofs of some previous results due to Kuusi–Mingione–Sire and Bass–Ren. Its flexibility is demonstrated by new applications to nonautonomous parabolic equations with nonlocal elliptic part and questions related to maximal regularity. |
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Keywords
Elliptic equations, fractional differentiability, nonlocal
and stable-like operators, self-improving properties,
analytic perturbation arguments, Cauchy problem for
nonlocal parabolic equations
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Mathematical Subject Classification 2010
Primary: 35D30, 35R11
Secondary: 26A33, 35K90, 46B70
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Milestones
Received: 6 August 2017
Accepted: 15 December 2017
Published: 14 May 2018
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Authors |
| Pascal Auscher | |
| Laboratoire de Mathematique
d’Orsay Université de Paris-Sud, CNRS Université Paris-Saclay 91405 Orsay France |
Laboratoire Amiénois de
Mathématiques Fondamentales et Appliquées UMR 7352 du CNRS Université de Picardie-Jules Verne 80039 Amiens France |
| Simon Bortz | |
| School of Mathematics University of Minnesota Minneapolis, MN 55455 United States |
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| Moritz Egert | |
| Laboratoire de Mathématiques
d’Orsay Université Paris-Sud, CNRS Université Paris-Saclay 91405 Orsay France |
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| Olli Saari | |
| Department of Mathematics and
Systems Analysis Aalto University P.O. Box 11100 FI-00076 Aalto Finland |
Mathematical Institute University of Bonn 53115 Bonn Germany |
