Shape Optimization Problems for Metric Graphs
type: Dataset
description: We consider the shape optimization problem min{E(Γ) : Γ∈A, H^1(Γ)=l }, where H^1 is the one-dimensional Hausdorff measure and A is an admissible class of one-dimensional sets connecting some prescribed set of points D={D_1,...,D_k}⊂Rd. The cost functional E(Γ) is the Dirichlet energy of Γ defined through the Sobolev functions on Γ vanishing on the points D_i. 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.
issued: 2026-05-07T03:32:38.403703
language: en
modified: 2026-05-07T03:32:38.403708
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticspreprint
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: preprints-working-papers-
landing page: https://hal.science/hal-00941094

Shape Optimization Problems for Metric Graphs
type: Distribution
format: HTML
issued: 2026-05-07T03:32:38.404808
modified: 2026-05-07T03:32:38.397671
access URL: https://hal.science/hal-00941094

test_moissonnage_selune
type: Agent