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arXiv · 2609.12967

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

Boyan Sirakov·Philippe Souplet
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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.

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Boyan Sirakov, Philippe Souplet. 2026-09-14. Differential Harnack inequalities and maximum principles of Morel-Oswald type for elliptic PDE in divergence form. https://arxiv.org/abs/2609.12967

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