Local Hopf Lemma for Certain Degenerate Elliptic Operators on the Half-Space

Hyungwoon Koo, Song Ying Li

Research output: Contribution to journalArticlepeer-review


We prove that the local Hopf lemma of Baouendi–Rothschild for harmonic functions continues to hold for the degenerate elliptic operator, Lα=xα∂x2+∑j=1n∂yj2 , on the half-space when the degeneracy exponent α is less than 2. We provide examples of degenerate elliptic operators with the degeneracy exponent greater or equals to 2 for which the local Hopf lemma fail.

Original languageEnglish
Article number67
JournalComplex Analysis and Operator Theory
Issue number5
Publication statusPublished - 2023 Jul

Bibliographical note

Funding Information:
H. Koo was supported by NRF of Korea (NRF-2022R1F1A1063305).

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.


  • Degenerate elliptic operator
  • Half-space
  • Local Hopf lemma

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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