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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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