Second-order boundary estimate for the solution to infinity Laplace equations
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Date
2017-07-24
Authors
Mi, Ling
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we establish a second-order estimate for the solutions to the infinity Laplace equation
-∆∞u = b(x)g(u), u > 0, x ∈ Ω, u|∂Ω = 0,
where Ω is a bounded domain in ℝN, g ∈ C1 ((0, ∞)), g is decreasing on (0, ∞) with lim s→0+ g(s) = ∞ and g is normalized regularly varying at zero with index -γ (γ > 1), b ∈ C(Ω̅) is positive in Ω, may be vanishing on the boundary. Our analysis is based on Karamata regular variation theory.
Description
Keywords
Infinity Laplace equation, Second order estimate, Karamata regular variation theory, Comparison functions
Citation
Mi, L. (2017). Second-order boundary estimate for the solution to infinity Laplace equations. Electronic Journal of Differential Equations, 2017(187), pp. 1-18.
Rights
Attribution 4.0 International