PreprintarXiv licencearXiv
Differential Harnack inequalities and maximum principles of Morel-Oswald type for elliptic PDE in divergence form
Abstract
This paper presents two types of novel, qualitative and quantitative, estimates for positive solutions of general uniformly elliptic PDEs in divergence form. First, we prove a Morel-Oswald type of extension of the Hopf-Oleinik lemma, in which in addition we specify the sharp dependence of the constant in the data of the operator and the size of the domain. Second, we establish a new differential Harnack (logarithmic gradient) estimate for non-homogeneous equations, as well as an optimal global differential Harnack estimate for homogeneous equations.
Related
- Harnack-type inequalities for nonlocal doubly nonlinear parabolic equations
- Characterization of intrinsic parabolic Harnack inequalities for doubly nonlinear equations of slow diffusion type
- Harnack-type inequalities for nonlocal parabolic equations in the upper fast-diffusion range
- Reverse Transportation and Harnack Inequalities for Underdamped Langevin in the Non-convex Setting
- Differential Harnack Estimates and Frequency Monotonicity for Filtration Equations on Riemannian Manifolds
BibTeX
@misc{sirakov2026differential,
title = {{Differential Harnack inequalities and maximum principles of Morel-Oswald type for elliptic PDE in divergence form}},
author = {Boyan Sirakov and Philippe Souplet},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12967},
eprint = {2609.12967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12967},
}
RIS
TY - UNPB
TI - Differential Harnack inequalities and maximum principles of Morel-Oswald type for elliptic PDE in divergence form
AU - Boyan Sirakov
AU - Philippe Souplet
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.12967
UR - https://arxiv.org/abs/2609.12967
AB - This paper presents two types of novel, qualitative and quantitative, estimates for positive solutions of general uniformly elliptic PDEs in divergence form. First, we prove a Morel-Oswald type of extension of the Hopf-Oleinik lemma, in which in addition we specify the sharp dependence of the constant in the data of the operator and the size of the domain. Second, we establish a new differential Harnack (logarithmic gradient) estimate for non-homogeneous equations, as well as an optimal global differential Harnack estimate for homogeneous equations.
ER -