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Optimal measures for the fundamental gapof Schrödinger operators

Published online by Cambridge University Press:  19 December 2008

Nicolas Varchon
Nicolas Varchon*
Affiliation:
Collège Condorcet de Bresles, Rue du Petit Chantilly, 60510 Bresles, France. nicolas.varchon@ac-amiens.fr
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Abstract

We study the potential which minimizes the fundamental gap of theSchrödinger operator under the total mass constraint. We considerthe relaxed potential and prove a regularity result for the optimalone, we also give a description of it. A consequence of this resultis the existence of an optimal potential under L 1 constraints.

Keywords

Schrödinger operatoreigenvalue problemsmeasuretheoryshape optimization
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 1 , January 2010 , pp. 194 - 205
Copyright
© EDP Sciences, SMAI, 2008

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