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arXiv · 2503.23272

Hopf-Oleinik lemma for elliptic equations in double divergence form

Hongjie Dong·Seick Kim·Boyan Sirakov
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Abstract

We establish, for the first time, a Zaremba-Hopf-Oleinik type boundary point lemma for uniformly elliptic partial differential equations in double divergence form, also known as stationary Fokker-Planck-Kolmogorov equations. As an application, we derive sharp two-sided estimates for the Green's function associated with second-order elliptic equations in non-divergence form in $C^{1,\alpha}$ domains.

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Hongjie Dong, Seick Kim, Boyan Sirakov. 2025-03-30. Hopf-Oleinik lemma for elliptic equations in double divergence form. https://arxiv.org/abs/2503.23272

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