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2020 Regularity estimates for elliptic nonlocal operators
Bartłomiej Dyda, Moritz Kassmann
Anal. PDE 13(2): 317-370 (2020). DOI: 10.2140/apde.2020.13.317

Abstract

We study weak solutions to nonlocal equations governed by integrodifferential operators. Solutions are defined with the help of symmetric nonlocal bilinear forms. Throughout this work, our main emphasis is on operators with general, possibly singular, measurable kernels. We obtain regularity results which are robust with respect to the differentiability order of the equation. Furthermore, we provide a general tool for the derivation of Hölder a priori estimates from the weak Harnack inequality. This tool is applicable for several local and nonlocal, linear and nonlinear problems on metric spaces. Another aim of this work is to provide comparability results for nonlocal quadratic forms.

Citation

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Bartłomiej Dyda. Moritz Kassmann. "Regularity estimates for elliptic nonlocal operators." Anal. PDE 13 (2) 317 - 370, 2020. https://doi.org/10.2140/apde.2020.13.317

Information

Received: 25 November 2015; Revised: 8 December 2017; Accepted: 9 April 2018; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07181503
MathSciNet: MR4078229
Digital Object Identifier: 10.2140/apde.2020.13.317

Subjects:
Primary: 31B05 , 35B05 , 35B45 , 35R11 , 47G20
Secondary: 60J75

Keywords: Hölder regularity estimates , nonlocal Dirichlet forms , weak Harnack inequality

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 2 • 2020
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