Dirichlet to Neumann maps for infinite quantum graphs

Robert Carlson

doi:10.3934/nhm.2012.7.483

Article Contents

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: September 2011

Revised: June 2012

Published: September 2012

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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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Mathematics Subject Classification: Primary: 34B45.

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References

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