PreprintCC BY 4.0arXiv
Hölder Gradient Estimates for (s,p)-Poisson Equations with measurable and Hölder Data
Abstract
We prove interior C1,α estimates for weak solutions of the fractional p-Poisson equation, with p≥2. For right-hand sides in Lq, we obtain the estimate when p<(1−d/q)/(1−s). For γ-Hölder continuous right-hand sides, the range is p<(1+γ)/(1−s). Both ranges of parameters are optimal.
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BibTeX
@misc{giovagnoli2026hölder,
title = {{Hölder Gradient Estimates for $(s,p)$-Poisson Equations with measurable and Hölder Data}},
author = {Davide Giovagnoli and David Jesus},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12012},
eprint = {2610.12012},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12012},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hölder Gradient Estimates for (s,p)-Poisson Equations with measurable and Hölder Data
AU - Davide Giovagnoli
AU - David Jesus
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12012
UR - https://arxiv.org/abs/2610.12012
AB - We prove interior C^1,α estimates for weak solutions of the fractional p-Poisson equation, with p≥2. For right-hand sides in L^q, we obtain the estimate when p<(1−d/q)/(1−s). For γ-Hölder continuous right-hand sides, the range is p<(1+γ)/(1−s). Both ranges of parameters are optimal.
ER -