PreprintCC BY-NC-ND 4.0arXiv
Nonlocal intrinsic Harnack estimates
Abstract
We extend DiBenedetto's intrinsic parabolic Harnack estimates to a class of integro-differential equations with measurable kernels modeled on the fractional p-Laplacian. More remarkably, we establish intrinsic, representation type nonlocal estimates and reveal that nonnegative local solutions abide by a strong maximum principle even for p>2, a property unique to nonlocal problems. Analogous results hold true for nonlocal equations of porous medium type.
Related
- Integral Harnack-type estimates and the rate of extinction for nonlocal doubly nonlinear parabolic equations
- Harnack-type estimates for nonlocal double phase functionals
- Harnack-type inequalities for nonlocal doubly nonlinear parabolic equations
- Harnack-type inequalities for nonlocal parabolic equations in the upper fast-diffusion range
- Characterization of intrinsic parabolic Harnack inequalities for doubly nonlinear equations of slow diffusion type
BibTeX
@misc{liao2026nonlocal,
title = {{Nonlocal intrinsic Harnack estimates}},
author = {Naian Liao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17400},
eprint = {2609.17400},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17400},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Nonlocal intrinsic Harnack estimates
AU - Naian Liao
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17400
UR - https://arxiv.org/abs/2609.17400
AB - We extend DiBenedetto's intrinsic parabolic Harnack estimates to a class of integro-differential equations with measurable kernels modeled on the fractional p-Laplacian. More remarkably, we establish intrinsic, representation type nonlocal estimates and reveal that nonnegative local solutions abide by a strong maximum principle even for p>2, a property unique to nonlocal problems. Analogous results hold true for nonlocal equations of porous medium type.
ER -