Second-order boundary estimate for the solution to infinity Laplace equations

Date

2017-07-24

Authors

Mi, Ling

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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.

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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. <i>Electronic Journal of Differential Equations, 2017</i>(187), pp. 1-18.

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Attribution 4.0 International

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