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measuretheory

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Optimal measures for the fundamental gapof Schrödinger operators
Nicolas Varchon
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 16 / Issue 1 / January 2010

Published online by Cambridge University Press:

19 December 2008, pp. 194-205

Print publication:

January 2010
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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.