Geodesic
A quantitative version of the Hopf–Oleinik lemma for a quasilinear non-uniformly elliptic operator
Diego Moreira1 ; Jefferson Abrantes Santos2 ; Sergio H. Monari Soares3
1 Universidade Federal do Ceará, Departamento de Matemática
2 Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática
3 Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 337–348.

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This paper establishes a quantitative version of the Hopf–Oleinik lemma (HOL) for a quasilinear non-uniformly elliptic operator of the form $\mathcal{L}_\infty u: =2\Delta_\infty u+\Delta u$. One key point in the proof is the passage from non-uniformly elliptic operators to locally uniformly ones via a new, uniform, and, rescaled version of the gradient estimate obtained by Evans and Smart for solutions to a family of non-uniformly quasilinear elliptic operators.  
DOI : 10.54330/afm.146035
Keywords: Hopf–Oleinik lemma, quasilinear non-uniformly elliptic operators

Diego Moreira 1 ; Jefferson Abrantes Santos 2 ; Sergio H. Monari Soares 3

1 Universidade Federal do Ceará, Departamento de Matemática
2 Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática
3 Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação 
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Diego Moreira; Jefferson Abrantes Santos; Sergio H. Monari Soares. A quantitative version of the Hopf–Oleinik lemma for a quasilinear non-uniformly elliptic operator. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 337–348. doi : 10.54330/afm.146035. http://geodesic.mathdoc.fr/articles/10.54330/afm.146035/

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