Nonlocal operators with singular anisotropic kernels

Chaker J, Kaßmann M (2019)
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck| Englisch
 
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Autor*in
Chaker, Jamil; Kaßmann, MoritzUniBi
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
ISSN
0360-5302
eISSN
1532-4133
Page URI
https://pub.uni-bielefeld.de/record/2939169

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Chaker J, Kaßmann M. Nonlocal operators with singular anisotropic kernels. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. 2019.
Chaker, J., & Kaßmann, M. (2019). Nonlocal operators with singular anisotropic kernels. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. doi:10.1080/03605302.2019.1651335
Chaker, J., and Kaßmann, M. (2019). Nonlocal operators with singular anisotropic kernels. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS.
Chaker, J., & Kaßmann, M., 2019. Nonlocal operators with singular anisotropic kernels. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS.
J. Chaker and M. Kaßmann, “Nonlocal operators with singular anisotropic kernels”, COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2019.
Chaker, J., Kaßmann, M.: Nonlocal operators with singular anisotropic kernels. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. (2019).
Chaker, Jamil, and Kaßmann, Moritz. “Nonlocal operators with singular anisotropic kernels”. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2019).