Harnack inequalities for supersolutions of fully nonlinear elliptic difference and differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:438

Article

Hamamuki, Nao¹ 

[1] Hokkaido Univ, Dept Math, Kita Ku, Kite 10,Nishi 8, Sapporo, Hokkaido 0600810, Japan

关键词: Harnack inequality;    Fully nonlinear elliptic equations;    Discrete solutions;    Viscosity solutions;   

DOI  :  10.1016/j.jmaa.2016.01.070

来源: Elsevier

【 摘 要 】

We present a new Harnack inequality for non-negative discrete supersolutions of fully nonlinear uniformly elliptic difference equations on rectangular lattices. This estimate applies to all supersolutions and has the Harnack constant depending on the graph distance on lattices: For the proof we modify the proof of the weak Harnack inequality. Applying the same idea to elliptic equations in a Euclidean space, we also derive a Harnack type inequality for non-negative viscosity supersolutions. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free