On the boundary estimates for second-order elliptic equations

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Consider uniformly elliptic equations in general form Lu = aijDiju + biDiui n a domain Ω ⊂ Rn, n ≥ 2.. We discuss the minimal assumptions on the boundary of Ω which guarantee the existence or non-existence of Hopf–Oleinik estimates for solutions, provided bi ∈ Lq(Ω),q > n.. The work is presented in a unified way based on a few basic facts from qualitative theory of elliptic equations.

Original languageEnglish (US)
Pages (from-to)1123-1141
Number of pages19
JournalComplex Variables and Elliptic Equations
Issue number7-8
StatePublished - Aug 3 2018

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Copyright 2018 Elsevier B.V., All rights reserved.


  • 35B45
  • 35J15
  • Elliptic equations
  • Hopf–Oleinik lemma
  • measurable coefficients


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