We consider optimization problems for cost functionals which depend on the negative spectrum of Schrödinger operators of the form , where is a potential, with prescribed compact support, which has to be determined. Under suitable assumptions the existence of an optimal potential is shown. This can be applied to interesting cases such as costs functions involving finitely many negative eigenvalues.
Accepté le :
DOI : 10.1051/cocv/2016009
Mots clés : Optimal potentials, Schrödinger operators, Lieb–Thirring inequality
@article{COCV_2017__23_2_627_0,
author = {Bouchitt\'e, Guy and Buttazzo, Giuseppe},
title = {Optimal design problems for {Schr\"odinger} operators with noncompact resolvents},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {627--635},
publisher = {EDP-Sciences},
volume = {23},
number = {2},
year = {2017},
doi = {10.1051/cocv/2016009},
mrnumber = {3608096},
zbl = {1358.49014},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2016009/}
}
TY - JOUR AU - Bouchitté, Guy AU - Buttazzo, Giuseppe TI - Optimal design problems for Schrödinger operators with noncompact resolvents JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 627 EP - 635 VL - 23 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2016009/ DO - 10.1051/cocv/2016009 LA - en ID - COCV_2017__23_2_627_0 ER -
%0 Journal Article %A Bouchitté, Guy %A Buttazzo, Giuseppe %T Optimal design problems for Schrödinger operators with noncompact resolvents %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 627-635 %V 23 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2016009/ %R 10.1051/cocv/2016009 %G en %F COCV_2017__23_2_627_0
Bouchitté, Guy; Buttazzo, Giuseppe. Optimal design problems for Schrödinger operators with noncompact resolvents. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 627-635. doi : 10.1051/cocv/2016009. http://www.numdam.org/articles/10.1051/cocv/2016009/
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