Geodesic
Optimal design problems for Schrödinger operators with noncompact resolvents
Bouchitté, Guy1  ; Buttazzo, Giuseppe2 
1 Laboratoire IMATH, Université de Toulon, BP 20132, 83957 La Garde cedex, France
2 Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 627-635

Voir la notice de l'article provenant de la source Numdam

We consider optimization problems for cost functionals which depend on the negative spectrum of Schrödinger operators of the form -Δ+V(x), where V 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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016009
Classification : 49J45, 35J10, 58C40, 49R05, 35P15
Keywords: Optimal potentials, Schrödinger operators, Lieb–Thirring inequality

Bouchitté, Guy 1 ; Buttazzo, Giuseppe 2

1 Laboratoire IMATH, Université de Toulon, BP 20132, 83957 La Garde cedex, France
2 Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :