Skip to main content

Shape optimization problems for metric graphs

  • Giuseppe Buttazzo (a1), Berardo Ruffini (a2) and Bozhidar Velichkov (a2)

We consider the shape optimization problem \hbox{$\min\big\{\E(\Gamma)\ :\ \Gamma\in\A,\ \H^1(\Gamma)=l\ \big\},$} min{ℰ(Γ):Γ ∈ 𝒜, ℋ1(Γ) = l}, where ℋ1 is the one-dimensional Hausdorff measure and 𝒜 is an admissible class of one-dimensional sets connecting some prescribed set of points \hbox{$\D=\{D_1,\dots,D_k\}\subset\R^d$} 𝒟 =  { D1,...,Dk }  ⊂ Rd. 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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

ESAIM: Control, Optimisation and Calculus of Variations
  • ISSN: 1292-8119
  • EISSN: 1262-3377
  • URL: /core/journals/esaim-control-optimisation-and-calculus-of-variations
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 4 *
Loading metrics...

Abstract views

Total abstract views: 51 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th April 2018. This data will be updated every 24 hours.