PreprintarXiv licencearXiv
Characterization of intrinsic parabolic Harnack inequalities for doubly nonlinear equations of slow diffusion type
Abstract
We characterize metric measure spaces that satisfy intrinsic parabolic Harnack inequalities for doubly nonlinear equations of slow diffusion type. The considered parabolic Harnack inequalities are intrinsic in the sense that the waiting time depends on the solution. Our main results shows that in a metric measure space with a doubling measure, such an intrinsic parabolic Harnack inequality holds if and only if a Poincaré inequality holds. We thus show that estimates in scale and function dependent intrinsic geometries can characterize scale and location invariant functional inequalities.
Related
- Harnack-type inequalities for nonlocal doubly nonlinear parabolic equations
- Parabolic Poincaré inequalities and maximal function estimates for systems of partial differential equations
- Harnack-type inequalities for nonlocal parabolic equations in the upper fast-diffusion range
- Liouville Theorems for Semilinear Parabolic Equations Involving the Nonlinear Gradient Term
- Integral Harnack-type estimates and the rate of extinction for nonlocal doubly nonlinear parabolic equations
BibTeX
@misc{elenius2026characterization,
title = {{Characterization of intrinsic parabolic Harnack inequalities for doubly nonlinear equations of slow diffusion type}},
author = {Theo Elenius},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32496},
eprint = {2610.32496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32496},
}
RIS
TY - UNPB
TI - Characterization of intrinsic parabolic Harnack inequalities for doubly nonlinear equations of slow diffusion type
AU - Theo Elenius
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32496
UR - https://arxiv.org/abs/2610.32496
AB - We characterize metric measure spaces that satisfy intrinsic parabolic Harnack inequalities for doubly nonlinear equations of slow diffusion type. The considered parabolic Harnack inequalities are intrinsic in the sense that the waiting time depends on the solution. Our main results shows that in a metric measure space with a doubling measure, such an intrinsic parabolic Harnack inequality holds if and only if a Poincaré inequality holds. We thus show that estimates in scale and function dependent intrinsic geometries can characterize scale and location invariant functional inequalities.
ER -