The normal derivative lemma and surrounding issues

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. © 2022 Russian Academy of Sciences (DoM), London Mathematical Society, IOP Publishing Limited.

Authors
Apushkinskaya D.E. , Nazarov A.I.
Journal
Russian Mathematical Surveys
Number of issue
2
Language
English
Pages
189-249
Status
Published
Link
External link
DOI
10.1070/RM10049
Volume
77
Year
2022
Organizations
  • 1 RUDN University, Russian Federation
  • 2 St Petersburg State University, Russian Federation
  • 3 St Petersburg Department, The Steklov Mathematical Institute, Russian Academy of Sciences, Russian Federation
Keywords
Aleksandrov-Bakelman maximum principle; Harnack inequality; Hopf- Oleinik lemma; normal derivative lemma; strong maximum principle
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