We consider the shape optimization problem , where is the one-dimensional Hausdorff measure and is an admissible class of one-dimensional sets connecting some prescribed set of points . The cost functional is the Dirichlet energy of defined through the Sobolev functions on vanishing on the points . 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.
Mots clés : shape optimization, rectifiable sets, metric graphs, quantum graphs, Dirichlet energy
@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}, pages = {1--22}, publisher = {EDP-Sciences}, volume = {20}, number = {1}, year = {2014}, doi = {10.1051/cocv/2013050}, mrnumber = {3182688}, zbl = {1286.49050}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2013050/} }
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 SP - 1 EP - 22 VL - 20 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2013050/ DO - 10.1051/cocv/2013050 LA - en ID - COCV_2014__20_1_1_0 ER -
%0 Journal Article %A Buttazzo, Giuseppe %A Ruffini, Berardo %A Velichkov, Bozhidar %T Shape optimization problems for metric graphs %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 1-22 %V 20 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2013050/ %R 10.1051/cocv/2013050 %G en %F 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/articles/10.1051/cocv/2013050/
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