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.
Shape Optimization Problems for Metric Graphs / Buttazzo G; Ruffini B; Velichkov B. - In: ESAIM. COCV. - ISSN 1292-8119. - STAMPA. - 20:1(2014), pp. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
