TY  - JOUR
AB  - 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.
DA  - 2021
DO  - 10.1007/s00526-020-01915-1
LA  - eng
IS  - 1
PY  - 2021
SN  - 0944-2669
T2  - Calculus of Variations and Partial Differential Equations
TI  - Higher Hölder regularity for nonlocal equations with irregular kernel
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29508297
Y2  - 2024-11-21T19:52:36
ER  -