Non-local self-improving properties: A functional analytic approach
Pascal Auscher, Simon Bortz, Moritz Egert, Olli Saari
TL;DR
This paper introduces a functional analytic method to establish self-improving regularity properties of solutions to linear non-local elliptic equations, simplifying proofs and enabling new applications.
Contribution
It provides a new, streamlined approach to prove self-improving properties and extends these results to non-autonomous parabolic equations with non-local elliptic components.
Findings
Simplified proofs of existing regularity results
Extension to non-autonomous parabolic equations
New insights into maximal regularity for non-local problems
Abstract
A functional analytic approach to obtaining self-improving properties of solutions to linear non-local 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 non-autonomous parabolic equations with non-local elliptic part and questions related to maximal regularity
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