Weak Hopf lemma for the invariant Laplacian and related elliptic operators

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1 Citation (Scopus)

Abstract

We obtain a weak version of the Hopf lemma for the invariant Laplacian on the unit ball of the complex n-space. We also show that our result is sharp in some sense. Motivated by this result, we also consider a class of degenerate elliptic operators with the degeneracy depending on the distance to the boundary of the domain. We study the dependence of the validity of Hopf lemma on the degree of degeneracy of the operator. We show that Hopf lemma holds if the degeneracy is small and fails in general if the degeneracy is large. What is more interesting is the critical case for which we show that certain weak version of Hopf lemma holds.

Original languageEnglish
Pages (from-to)576-588
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume408
Issue number2
DOIs
Publication statusPublished - 2013 Dec 15

Keywords

  • Degenerating elliptic operator
  • Hopf lemma
  • Invariant Laplacian

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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