Determining sets for the discrete Laplacian

被引：1

作者：

Rubinstein, Aviad ^{[1
]}

Rubinstein, Jacob ^{[1
]}

Wolansky, Gershon ^{[1
]}

机构：

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

来源：

SIAM REVIEW | 2007年 / 49卷 / 02期

关键词：

Laplacian; determining sets; uniqueness;

D O I：

10.1137/050645233

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define a notion of determining sets for the discrete Laplacian in a domain Omega. A set D is called determining if harmonic functions are uniquely determined by providing their values on D, and if D has the same size as the boundary of Omega. It is shown that there exist determining sets that are fairly evenly distributed in Omega. A number of basic properties of determining sets are derived.

引用

页码：315 / 324

页数：10

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