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Regularity estimates
for elliptic nonlocal operators
Bartłomiej Dyda and Moritz Kassmann |
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Vol. 13 (2020), No. 2, 317–370
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Abstract |
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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. |
Keywords
nonlocal Dirichlet forms, Hölder regularity estimates, weak
Harnack inequality
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Mathematical Subject Classification 2010
Primary: 31B05, 35B05, 35B45, 35R11, 47G20
Secondary: 60J75
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Milestones
Received: 25 November 2015
Revised: 8 December 2017
Accepted: 9 April 2018
Published: 19 March 2020
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Authors |
| Bartłomiej Dyda | |
| Department of Pure and Applied
Mathematics Wrocław University of Science and Technology Wrocław Poland |
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| Moritz Kassmann | |
| Fakultät für Mathematik Universität Bielefeld Bielefeld Germany |
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