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

Hyungwoon Koo; Song Ying Li

doi:10.1007/s11785-023-01368-2

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

Hyungwoon Koo, Song Ying Li

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Article number	67
Journal	Complex Analysis and Operator Theory
Volume	17
Issue number	5
DOIs	https://doi.org/10.1007/s11785-023-01368-2
Publication status	Published - 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.

Keywords

Degenerate elliptic operator
Half-space
Local Hopf lemma

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s11785-023-01368-2

Cite this

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abstract = "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.",

keywords = "Degenerate elliptic operator, Half-space, Local Hopf lemma",

author = "Hyungwoon Koo and Li, {Song Ying}",

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N2 - 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.

AB - 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.

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KW - Local Hopf lemma

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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