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Rendiconti Lincei - Matematica e Applicazioni

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Volume 30, Issue 4, 2019, pp. 677–699
DOI: 10.4171/RLM/867

Published online: 2019-11-05

On the Boundary Point Principle for divergence-type equations

Darya E. Apushkinskaya[1] and Alexander I. Nazarov[2]

(1) Universität des Saarlandes, Saarbrücken, Germany and Peoples' Friendship Univ. of Russia, Moscow, Russia, and St. Peters
(2) Steklov Institute and St. Petersburg State University, Russia

We provide some versions of the Zaremba–Hopf–Oleinik boundary point lemma for general elliptic and parabolic equations in divergence form under the sharp requirements on the coefficients of equations and on the boundaries of domains.

Keywords: Hopf–Oleinik lemma, divergence-type equations, Dini continuity, Kato class

Apushkinskaya Darya, Nazarov Alexander: On the Boundary Point Principle for divergence-type equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), 677-699. doi: 10.4171/RLM/867