Calculus of Variations and Geometric Measure Theory
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G. Buttazzo - A. Gerolin - B. Ruffini - B. Velichkov

Optimal Potentials for Schrödinger Operators

created by gerolin on 02 May 2013
modified by velichkov on 27 Sep 2015

[BibTeX]

Published Paper

Inserted: 2 may 2013
Last Updated: 27 sep 2015

Journal: Journal de l'École polytechnique — Mathématiques (JEP)
Year: 2013

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 $V\geq 0$ has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.

Keywords: spectral optimization, Schrodinger operators, Optimal potentials


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