We consider the shape optimization problem 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 d connecting some prescribed set of points D = {D1,...,Dk} ⊂ R . 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.

Buttazzo G, Ruffini B, Velichkov B (2014). Shape Optimization Problems for Metric Graphs. ESAIM. COCV, 20(1), 1-22 [10.1051/cocv/2013050].

Shape Optimization Problems for Metric Graphs

Ruffini B;
2014

Abstract

We consider the shape optimization problem 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 d connecting some prescribed set of points D = {D1,...,Dk} ⊂ R . 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.
2014
Buttazzo G, Ruffini B, Velichkov B (2014). Shape Optimization Problems for Metric Graphs. ESAIM. COCV, 20(1), 1-22 [10.1051/cocv/2013050].
Buttazzo G; Ruffini B; Velichkov B
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/733113
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