Optimal potentials for Schrödinger operators

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

Journal de l’École polytechnique — Mathématiques (2014)

  • Volume: 1, page 71-100
  • ISSN: 2270-518X

Abstract

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

How to cite

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Buttazzo, Giuseppe, et al. "Optimal potentials for Schrödinger operators." Journal de l’École polytechnique — Mathématiques 1 (2014): 71-100. <http://eudml.org/doc/275470>.

@article{Buttazzo2014,
abstract = {We consider the Schrödinger operator $-\Delta +V(x)$ on $H^1_0(\Omega )$, where $\Omega $ is a given domain of $\mathbb\{R\}^d$. Our goal is to study some optimization problems where an optimal potential $V\ge 0$ has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.},
affiliation = {Dipartimento di Matematica, Università di Pisa Largo B. Pontecorvo 5, 56127 Pisa, Italy; Dipartimento di Matematica, Università di Pisa Largo B. Pontecorvo 5, 56127 Pisa, Italy; Laboratoire Jean Kuntzmann, Université de Grenoble BP 53, 38041 Grenoble Cedex 9, France; Dipartimento di Matematica, Università di Pisa Largo B. Pontecorvo 5, 56127 Pisa, Italy},
author = {Buttazzo, Giuseppe, Gerolin, Augusto, Ruffini, Berardo, Velichkov, Bozhidar},
journal = {Journal de l’École polytechnique — Mathématiques},
keywords = {Schrödinger operators; optimal potentials; spectral optimization; capacity},
language = {eng},
pages = {71-100},
publisher = {École polytechnique},
title = {Optimal potentials for Schrödinger operators},
url = {http://eudml.org/doc/275470},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Buttazzo, Giuseppe
AU - Gerolin, Augusto
AU - Ruffini, Berardo
AU - Velichkov, Bozhidar
TI - Optimal potentials for Schrödinger operators
JO - Journal de l’École polytechnique — Mathématiques
PY - 2014
PB - École polytechnique
VL - 1
SP - 71
EP - 100
AB - We consider the Schrödinger operator $-\Delta +V(x)$ on $H^1_0(\Omega )$, where $\Omega $ is a given domain of $\mathbb{R}^d$. Our goal is to study some optimization problems where an optimal potential $V\ge 0$ has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.
LA - eng
KW - Schrödinger operators; optimal potentials; spectral optimization; capacity
UR - http://eudml.org/doc/275470
ER -

References

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