Nonlinear nonlocal potential theory at the gradient level
Diening L, Kim K, Lee H-S, Nowak SN (2024)
arXiv:2402.04809.
Preprint | Englisch
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Abstract / Bemerkung
The aim of this work is to establish numerous interrelated gradient estimates
in the nonlinear nonlocal setting. First of all, we prove that weak solutions
to a class of homogeneous nonlinear nonlocal equations of possibly arbitrarily
low order have Hölder continuous gradients. Using these estimates in the
homogeneous case, we then prove sharp higher differentiability as well as
pointwise gradient potential estimates for nonlinear nonlocal equations of
order larger than one in the presence of general measure data. Our pointwise
estimates imply that the first-order regularity properties of such nonlinear
nonlocal equations coincide with the sharp ones of the fractional Laplacian.
Erscheinungsjahr
2024
Zeitschriftentitel
arXiv:2402.04809
Page URI
https://pub.uni-bielefeld.de/record/2986868
Zitieren
Diening L, Kim K, Lee H-S, Nowak SN. Nonlinear nonlocal potential theory at the gradient level. arXiv:2402.04809. 2024.
Diening, L., Kim, K., Lee, H. - S., & Nowak, S. N. (2024). Nonlinear nonlocal potential theory at the gradient level. arXiv:2402.04809. https://doi.org/10.48550/ARXIV.2402.04809
Diening, Lars, Kim, Kyeongbae, Lee, Ho-Sik, and Nowak, Simon Noah. 2024. “Nonlinear nonlocal potential theory at the gradient level”. arXiv:2402.04809.
Diening, L., Kim, K., Lee, H. - S., and Nowak, S. N. (2024). Nonlinear nonlocal potential theory at the gradient level. arXiv:2402.04809.
Diening, L., et al., 2024. Nonlinear nonlocal potential theory at the gradient level. arXiv:2402.04809.
L. Diening, et al., “Nonlinear nonlocal potential theory at the gradient level”, arXiv:2402.04809, 2024.
Diening, L., Kim, K., Lee, H.-S., Nowak, S.N.: Nonlinear nonlocal potential theory at the gradient level. arXiv:2402.04809. (2024).
Diening, Lars, Kim, Kyeongbae, Lee, Ho-Sik, and Nowak, Simon Noah. “Nonlinear nonlocal potential theory at the gradient level”. arXiv:2402.04809 (2024).