Volume 20, Number 1, January-March 2014
|Page(s)||1 - 22|
|Published online||29 August 2013|
Shape optimization problems for metric graphs
Dipartimento di Matematica, Università di Pisa,
Largo B. Pontecorvo 5,
2 Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy
Revised: 18 December 2012
We consider the shape optimization problem where ℋ1 is the one-dimensional Hausdorff measure and 𝒜 is an admissible class of one-dimensional sets connecting some prescribed set of points . The cost functional ℰ(Γ) is the Dirichlet energy of Γ defined through the Sobolev functions on Γ vanishing on the points Di. We analyze the existence of a solution in both the families of connected sets and of metric graphs. At the end, several explicit examples are discussed.
Mathematics Subject Classification: 49R05 / 49Q20 / 49J45 / 81Q35
Key words: Shape optimization / rectifiable sets / metric graphs / quantum graphs / Dirichlet energy
© EDP Sciences, SMAI, 2013
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