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JOURNALS // Uspekhi Matematicheskikh Nauk // Archive

Uspekhi Mat. Nauk, 2022 Volume 77, Issue 2(464), Pages 3–68 (Mi rm10049)

This article is cited in 17 papers

The normal derivative lemma and surrounding issues

D. E. Apushkinskayaab, A. I. Nazarovcb

a RUDN University
b St Petersburg State University
c St Petersburg Department of the Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: In this survey we describe the history and current state of one of the key areas in the qualitative theory of elliptic partial differential equations related to the strong maximum principle and the boundary point principle (normal derivative lemma).
Bibliography: 234 titles.

Keywords: strong maximum principle, normal derivative lemma, Hopf–Oleinik lemma, Harnack inequality, Aleksandrov–Bakelman maximum principle.

UDC: 517.95

MSC: Primary 35-02, 35B45, 35B50, 35J15; Secondary 35R05

Received: 19.07.2021

DOI: 10.4213/rm10049


 English version:
Russian Mathematical Surveys, 2022, 77:2, 189–249

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© Steklov Math. Inst. of RAS, 2025