Shape optimization problems for metric graphs
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 1, p. 1-22
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We consider the shape optimization problem min { ( Γ ) : Γ 𝒜 , 1 ( Γ ) = l } , where 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 } d . The cost functional ( 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.
DOI : https://doi.org/10.1051/cocv/2013050
Classification:  49R05,  49Q20,  49J45,  81Q35
@article{COCV_2014__20_1_1_0,
     author = {Buttazzo, Giuseppe and Ruffini, Berardo and Velichkov, Bozhidar},
     title = {Shape optimization problems for metric graphs},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {1},
     year = {2014},
     pages = {1-22},
     doi = {10.1051/cocv/2013050},
     zbl = {1286.49050},
     mrnumber = {3182688},
     language = {en},
     url = {http://http://www.numdam.org/item/COCV_2014__20_1_1_0}
}
Buttazzo, Giuseppe; Ruffini, Berardo; Velichkov, Bozhidar. Shape optimization problems for metric graphs. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 1, pp. 1-22. doi : 10.1051/cocv/2013050. http://www.numdam.org/item/COCV_2014__20_1_1_0/

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