Work

Differential Harnack inequalities and maximum principles of Morel-Oswald type for elliptic PDE in divergence form

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.12967

Authors: Sirakov, Boyan, Souplet, Philippe

Institutions: Centre National de la Recherche Scientifique, Pontifícia Universidade Católica do Rio de Janeiro, Université Sorbonne Paris Nord, Laboratoire Analyse, Géométrie et Applications

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Pontifícia Universidade Católica do Rio de Janeiro

OpenAlex ID: W7213304363

Cites:

Cited by: 1

Related to: 10