A DISCRETE HARMONIC FUNCTION BOUNDED ON A LARGE PORTION OF Z2 IS CONSTANT

被引：4

作者：

Buhovsky, Lev ^{[1
]}

Logunov, Alexander ^{[2
,3
]}

Malinnikova, Eugenia ^{[4
,5
]}

Sodin, Mikhail ^{[1
]}

机构：

[1] Tel Aviv Univ, Sch Math Sci, Tel Aviv, Israel

[2] Univ Geneva, Sect Math, Geneva, Switzerland

[3] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[4] Norwegian Univ Sci & Technol, Dept Math Sci, Trondheim, Norway

[5] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

DUKE MATHEMATICAL JOURNAL | 2022年 / 171卷 / 06期

基金：

欧洲研究理事会; 以色列科学基金会;

关键词：

D O I：

10.1215/00127094-2021-0037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An improvement of the Liouville theorem for discrete harmonic functions on Z(2) is obtained. More precisely, we prove that there exists a positive constant epsilon such that if u is discrete harmonic on Z(2) and for each sufficiently large square Q centered at the origin vertical bar u vertical bar <= 1 on a (1 - epsilon) portion of Q, then u is constant.

引用

页码：1349 / 1378

页数：30

共 18 条

[1] ELEMENTARY PROOF OF THE REMEZ INEQUALITY [J].