PreprintarXiv licencearXiv
Hölder regularity for nonlocal equations governed by measures and non-standard growth
Abstract
On doubling metric measure spaces, we study nonlocal operators with non-standard (p,q)-Orlicz growth (1<p≤ q<∞), where the interaction kernel is given by a general, non-translation-invariant measure. Under natural assumptions on the interaction measure - namely symmetry, a suitable nonlocal Poincaré inequality, and a tail bound - we prove that every weak solution to the corresponding homogeneous nonlocal equation admits a locally Hölder continuous representative. These regularity results are new even in the Euclidean setting.
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BibTeX
@misc{schleef2026hölder,
title = {{Hölder regularity for nonlocal equations governed by measures and non-standard growth}},
author = {Luke Schleef},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28336},
eprint = {2608.28336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28336},
}
RIS
TY - UNPB
TI - Hölder regularity for nonlocal equations governed by measures and non-standard growth
AU - Luke Schleef
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28336
UR - https://arxiv.org/abs/2608.28336
AB - On doubling metric measure spaces, we study nonlocal operators with non-standard (p,q)-Orlicz growth (1<p≤ q<∞), where the interaction kernel is given by a general, non-translation-invariant measure. Under natural assumptions on the interaction measure - namely symmetry, a suitable nonlocal Poincaré inequality, and a tail bound - we prove that every weak solution to the corresponding homogeneous nonlocal equation admits a locally Hölder continuous representative. These regularity results are new even in the Euclidean setting.
ER -