Optimal potentials for Schrödinger operators
[Potentiels optimaux pour les opérateurs de Schrödinger]
Journal de l’École polytechnique — Mathématiques, Tome 1 (2014), pp. 71-100.

Nous considérons l’opérateur de Schrödinger -Δ+V(x) sur H 0 1 (Ω), où Ω est un domaine fixé de d . Nous étudions certains problèmes d’optimisation pour lesquels un potentiel optimal V0 doit être déterminé dans une certaine classe admissible et pour certains critères d’optimisation tels que l’énergie ou les valeurs propres de Dirichlet.

We consider the Schrödinger operator -Δ+V(x) on H 0 1 (Ω), where Ω is a given domain of d . Our goal is to study some optimization problems where an optimal potential V0 has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.

DOI : https://doi.org/10.5802/jep.4
Classification : 49J45,  35J10,  49R05,  35P15,  35J05
Mots clés : Opérateurs de Schrödinger, potentiels optimaux, optimisation spectrale, capacité
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     author = {Buttazzo, Giuseppe and Gerolin, Augusto and Ruffini, Berardo and Velichkov, Bozhidar},
     title = {Optimal potentials for {Schr\"odinger~operators}},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
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     publisher = {Ecole polytechnique},
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     year = {2014},
     doi = {10.5802/jep.4},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jep.4/}
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Buttazzo, Giuseppe; Gerolin, Augusto; Ruffini, Berardo; Velichkov, Bozhidar. Optimal potentials for Schrödinger operators. Journal de l’École polytechnique — Mathématiques, Tome 1 (2014), pp. 71-100. doi : 10.5802/jep.4. http://www.numdam.org/articles/10.5802/jep.4/

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