This paper establishes a quantitative version of the Hopf–Oleinik lemma (HOL)for a quasilinear non-uniformly elliptic operator of the formL∞u:= 2∆∞u+ ∆u. One key point inthe 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 solutionsto a family of non-uniformly quasilinear elliptic operators.
Moreira, D., Santos, J.A., Soares, S.H.M. (2024). A quantitative version of the Hopf–Oleinik lemma for a quasilinear non-uniformly elliptic operator. ANNALES FENNICI MATHEMATICI, 49(1), 337-348 [10.54330/afm.146035].
A quantitative version of the Hopf–Oleinik lemma for a quasilinear non-uniformly elliptic operator
Moreira, Diego;
2024
Abstract
This paper establishes a quantitative version of the Hopf–Oleinik lemma (HOL)for a quasilinear non-uniformly elliptic operator of the formL∞u:= 2∆∞u+ ∆u. One key point inthe 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 solutionsto a family of non-uniformly quasilinear elliptic operators.| File | Dimensione | Formato | |
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