Nonlocal operators with singular anisotropic kernels
Chaker J, Kaßmann M (2019)
Communications in Partial Differential Equations 45(1): 1-31.
Zeitschriftenaufsatz
| E-Veröff. vor dem Druck | Englisch
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Autor*in
Chaker, Jamil;
Kaßmann, MoritzUniBi 
Einrichtung
Abstract / Bemerkung
We study nonlocal operators acting on functions in the Euclidean space. The operators under consideration generate anisotropic jump processes, e.g., a jump process that behaves like a stable process in each direction but with a different index of stability. Its generator is the sum of one-dimensional fractional Laplace operators with different orders of differentiability. We study such operators in the general framework of bounded measurable coefficients. We prove a weak Harnack inequality and Holder regularity results for solutions to corresponding integro-differential equations.
Stichworte
Anisotropic measure;
energy form;
jump process;
nonlocal operator;
regularity;
weak Harnack inequality
Erscheinungsjahr
2019
Zeitschriftentitel
Communications in Partial Differential Equations
Band
45
Ausgabe
1
Seite(n)
1-31
ISSN
0360-5302
eISSN
1532-4133
Page URI
https://pub.uni-bielefeld.de/record/2939169
Zitieren
Chaker J, Kaßmann M. Nonlocal operators with singular anisotropic kernels. Communications in Partial Differential Equations . 2019;45(1):1-31.
Chaker, J., & Kaßmann, M. (2019). Nonlocal operators with singular anisotropic kernels. Communications in Partial Differential Equations , 45(1), 1-31. https://doi.org/10.1080/03605302.2019.1651335
Chaker, Jamil, and Kaßmann, Moritz. 2019. “Nonlocal operators with singular anisotropic kernels”. Communications in Partial Differential Equations 45 (1): 1-31.
Chaker, J., and Kaßmann, M. (2019). Nonlocal operators with singular anisotropic kernels. Communications in Partial Differential Equations 45, 1-31.
Chaker, J., & Kaßmann, M., 2019. Nonlocal operators with singular anisotropic kernels. Communications in Partial Differential Equations , 45(1), p 1-31.
J. Chaker and M. Kaßmann, “Nonlocal operators with singular anisotropic kernels”, Communications in Partial Differential Equations , vol. 45, 2019, pp. 1-31.
Chaker, J., Kaßmann, M.: Nonlocal operators with singular anisotropic kernels. Communications in Partial Differential Equations . 45, 1-31 (2019).
Chaker, Jamil, and Kaßmann, Moritz. “Nonlocal operators with singular anisotropic kernels”. Communications in Partial Differential Equations 45.1 (2019): 1-31.
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