# Shape optimization problems for metric graphs

Giuseppe Buttazzo; Berardo Ruffini; Bozhidar Velichkov

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 1, page 1-22
- ISSN: 1292-8119

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topButtazzo, Giuseppe, Ruffini, Berardo, and Velichkov, Bozhidar. "Shape optimization problems for metric graphs." ESAIM: Control, Optimisation and Calculus of Variations 20.1 (2014): 1-22. <http://eudml.org/doc/272872>.

@article{Buttazzo2014,

abstract = {Γ):Γ ∈ 𝒜, ℋ1(Γ) = l\}, where ℋ1D1,...,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.},

author = {Buttazzo, Giuseppe, Ruffini, Berardo, Velichkov, Bozhidar},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {shape optimization; rectifiable sets; metric graphs; quantum graphs; Dirichlet energy},

language = {eng},

number = {1},

pages = {1-22},

publisher = {EDP-Sciences},

title = {Shape optimization problems for metric graphs},

url = {http://eudml.org/doc/272872},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Buttazzo, Giuseppe

AU - Ruffini, Berardo

AU - Velichkov, Bozhidar

TI - Shape optimization problems for metric graphs

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 1

SP - 1

EP - 22

AB - Γ):Γ ∈ 𝒜, ℋ1(Γ) = l}, where ℋ1D1,...,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.

LA - eng

KW - shape optimization; rectifiable sets; metric graphs; quantum graphs; Dirichlet energy

UR - http://eudml.org/doc/272872

ER -

## References

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