Optimal potentials for Schrödinger operators
Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 71-100.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.4
Classification: 49J45, 35J10, 49R05, 35P15, 35J05
Keywords: Schrödinger operators, optimal potentials, spectral optimization, capacity
Mot clés : Opérateurs de Schrödinger, potentiels optimaux, optimisation spectrale, capacité
Giuseppe Buttazzo 1; Augusto Gerolin 1; Berardo Ruffini 2; Bozhidar Velichkov 1

1 Dipartimento di Matematica, Università di Pisa Largo B. Pontecorvo 5, 56127 Pisa, Italy
2 Laboratoire Jean Kuntzmann, Université de Grenoble BP 53, 38041 Grenoble Cedex 9, France
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Giuseppe Buttazzo; Augusto Gerolin; Berardo Ruffini; Bozhidar Velichkov. Optimal potentials for Schrödinger operators. Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 71-100. doi : 10.5802/jep.4. https://jep.centre-mersenne.org/articles/10.5802/jep.4/

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