PreprintCC BY 4.0arXiv
Sharp regularity for the anisotropic fractional Laplacian with Morrey data
Abstract
We obtain sharp regularity for the anisotropic fractional Laplace equation with a right-hand side belonging to a Morrey space. We derive local Cσ+λ−n−regularity of solutions when σ+λ−n≠1, where σ∈(0,2) is the order of the operator and λ∈(n−σ,n) is the Morrey decay rate of the right-hand side. In the case σ+λ−n=1, we show that solutions are locally in the Zygmund class, and hence are Log-Lipschitz continuous. Explicit examples attest to the sharpness of the conditions.
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BibTeX
@misc{teymurazyan2026sharp,
title = {{Sharp regularity for the anisotropic fractional Laplacian with Morrey data}},
author = {Rafayel Teymurazyan and José Miguel Urbano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39947},
eprint = {2610.39947},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39947},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp regularity for the anisotropic fractional Laplacian with Morrey data
AU - Rafayel Teymurazyan
AU - José Miguel Urbano
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39947
UR - https://arxiv.org/abs/2610.39947
AB - We obtain sharp regularity for the anisotropic fractional Laplace equation with a right-hand side belonging to a Morrey space. We derive local C^σ+λ−n−regularity of solutions when σ+λ−n≠1, where σ∈(0,2) is the order of the operator and λ∈(n−σ,n) is the Morrey decay rate of the right-hand side. In the case σ+λ−n=1, we show that solutions are locally in the Zygmund class, and hence are Log-Lipschitz continuous. Explicit examples attest to the sharpness of the conditions.
ER -