Higher Hölder regularity for nonlocal equations with irregular kernel

Nowak SN (2021)
Calculus of Variations and Partial Differential Equations 60(1): 24.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Abstract - We study the higher Hölder regularity of local weak solutions to a class of nonlinear nonlocal elliptic equations with kernels that satisfy a mild continuity assumption. An interesting feature of our main result is that the obtained regularity is better than one might expect when considering corresponding results for local elliptic equations in divergence form with continuous coefficients. Therefore, in some sense our result can be considered to be of purely nonlocal type, following the trend of various such purely nonlocal phenomena observed in recent years. Our approach can be summarized as follows. First, we use certain test functions that involve discrete fractional derivatives in order to obtain higher Hölder regularity for homogeneous equations driven by a locally translation invariant kernel, while the global behaviour of the kernel is allowed to be more general. This enables us to deduce the desired regularity in the general case by an approximation argument.
Erscheinungsjahr
2021
Zeitschriftentitel
Calculus of Variations and Partial Differential Equations
Band
60
Ausgabe
1
Art.-Nr.
24
ISSN
0944-2669
eISSN
1432-0835
Page URI
https://pub.uni-bielefeld.de/record/2950829

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Nowak SN. Higher Hölder regularity for nonlocal equations with irregular kernel. Calculus of Variations and Partial Differential Equations. 2021;60(1): 24.
Nowak, S. N. (2021). Higher Hölder regularity for nonlocal equations with irregular kernel. Calculus of Variations and Partial Differential Equations, 60(1), 24. doi:10.1007/s00526-020-01915-1
Nowak, S. N. (2021). Higher Hölder regularity for nonlocal equations with irregular kernel. Calculus of Variations and Partial Differential Equations 60:24.
Nowak, S.N., 2021. Higher Hölder regularity for nonlocal equations with irregular kernel. Calculus of Variations and Partial Differential Equations, 60(1): 24.
S.N. Nowak, “Higher Hölder regularity for nonlocal equations with irregular kernel”, Calculus of Variations and Partial Differential Equations, vol. 60, 2021, : 24.
Nowak, S.N.: Higher Hölder regularity for nonlocal equations with irregular kernel. Calculus of Variations and Partial Differential Equations. 60, : 24 (2021).
Nowak, Simon Noah. “Higher Hölder regularity for nonlocal equations with irregular kernel”. Calculus of Variations and Partial Differential Equations 60.1 (2021): 24.

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