Dirichlet to Neumann maps for infinite quantum graphs

Robert Carlson; Robert Carlson

doi:10.3934/nhm.2012.7.483

Networks and Heterogeneous Media

2012, Volume 7, Issue 3: 483-501. doi: 10.3934/nhm.2012.7.483

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Dirichlet to Neumann maps for infinite quantum graphs

Robert Carlson ^{1
,}

1.
Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, CO 80933

Received: 01 September 2011 Revised: 01 June 2012
Primary: 34B45.

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.
- Dirichlet problem,
- Dirichlet to Neumann map,
- infinite graph,
- network boundary problems,
- quantum graph
Citation: Robert Carlson. Dirichlet to Neumann maps for infinite quantum graphs[J]. Networks and Heterogeneous Media, 2012, 7(3): 483-501. doi: 10.3934/nhm.2012.7.483

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Abstract

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.

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