The Harnack Inequality for ∞-Harmonic Functions
The Harnack Inequality for ∞-Harmonic Functions
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发表时间：
1995-04
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通讯作者：
P. Lindqvist;J. Manfredi
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文献类型：
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作者：
P. Lindqvist;J. Manfredi
证明了方程∞u = 0的非负粘性解的Harnack不等式，推广了L.C.埃文斯的平滑解决方案。证明的方法是考虑当p→∞时，更常见的p-调和方程<$pu = 0的极限是<$∞u = 0。本文证明了∞−调和方程非负粘性解的Harnack不等式
The Harnack inequality for nonnegative viscosity solutions of the equation ∆∞u = 0 is proved, extending a previous result of L.C. Evans for smooth solutions. The method of proof consists in considering ∆∞u = 0 as the limit as p→∞ of the more familiar p-harmonic equation ∆pu = 0. The purpose of this note is to present a proof of the Harnack inequality for nonnegative viscosity solutions of the ∞−harmonic equation