Regularity estimates for elliptic nonlocal operators

Dyda B, Kaßmann M (2020)
Analysis & PDE 13(2): 317-370.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Dyda, Bartlomiej; Kaßmann, MoritzUniBi
Abstract / Bemerkung
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 Holder 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.
Stichworte
nonlocal Dirichlet forms; Holder regularity estimates; weak Harnack; inequality
Erscheinungsjahr
2020
Zeitschriftentitel
Analysis & PDE
Band
13
Ausgabe
2
Seite(n)
317-370
ISSN
1948-206X
Page URI
https://pub.uni-bielefeld.de/record/2942740

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Dyda B, Kaßmann M. Regularity estimates for elliptic nonlocal operators. Analysis & PDE . 2020;13(2):317-370.
Dyda, B., & Kaßmann, M. (2020). Regularity estimates for elliptic nonlocal operators. Analysis & PDE , 13(2), 317-370. https://doi.org/10.2140/apde.2020.13.317
Dyda, B., and Kaßmann, M. (2020). Regularity estimates for elliptic nonlocal operators. Analysis & PDE 13, 317-370.
Dyda, B., & Kaßmann, M., 2020. Regularity estimates for elliptic nonlocal operators. Analysis & PDE , 13(2), p 317-370.
B. Dyda and M. Kaßmann, “Regularity estimates for elliptic nonlocal operators”, Analysis & PDE , vol. 13, 2020, pp. 317-370.
Dyda, B., Kaßmann, M.: Regularity estimates for elliptic nonlocal operators. Analysis & PDE . 13, 317-370 (2020).
Dyda, Bartlomiej, and Kaßmann, Moritz. “Regularity estimates for elliptic nonlocal operators”. Analysis & PDE 13.2 (2020): 317-370.

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