DIRICHLET TO NEUMANN MAPS FOR INFINITE QUANTUM GRAPHS

被引：4
作者：
Carlson, Robert [1 ]
机构：
[1] Univ Colorado Colorado Springs, Dept Math, Colorado Springs, CO 80933 USA
来源：
NETWORKS AND HETEROGENEOUS MEDIA | 2012年 / 7卷 / 03期
关键词：
Dirichlet problem; Dirichlet to Neumann map; infinite graph; network boundary problems; quantum graph; BOUNDARY; TREES;
D O I：
10.3934/nhm.2012.7.483
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Dirichlet problem and Dirichlet to Neumann map are analyzed for elliptic equations on a large collection of infinite quantum graphs. For a dense set of continuous functions on the graph boundary, the Dirichlet to Neumann map has values in the Radon measures on the graph boundary.
引用
收藏
页码：483 / 501
页数：19
相关论文
共 31 条
[1]  
[Anonymous], PROBABILITY TR UNPUB
[2]  
[Anonymous], ARXIV08063881
[3]  
[Anonymous], 1984, Random walks and electric networks
[4]  
[Anonymous], 1971, CONV CALC PROB
[5]   Steklov eigenproblems and the representation of solutions of elliptic boundary value problems [J].
Auchmuty, G .
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2004, 25 (3-4) :321-348
[6]  
Avdonin S, 2008, INVERSE PROBL IMAG, V2, P1
[7]   Boundary spectral inverse problem on a class of graphs (trees) by the BC method [J].
Belishev, MI .
INVERSE PROBLEMS, 2004, 20 (03) :647-672
[8]   A Borg-Levinson theorem for trees [J].
Brown, BM ;
Weikard, R .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2005, 461 (2062) :3231-3243
[9]  
Calderón AP, 2006, COMPUT APPL MATH, V25, P133
[10]  
Carlson R., ARXIV11093137
1234