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Optimal measures for the fundamental gap of Schrödinger operators

Nicolas Varchon — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We study the potential which minimizes the fundamental gap of the Schrödinger operator under the total mass constraint. We consider the relaxed potential and prove a regularity result for the optimal one, we also give a description of it. A consequence of this result is the existence of an optimal potential under constraints.

Asymptotics of an optimal compliance-location problem

Giuseppe ButtazzoFilippo SantambrogioNicolas Varchon — 2006

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of placing a Dirichlet region made by small balls of given radius in a given domain subject to a force in order to minimize the compliance of the configuration. Then we let tend to infinity and look for the Γ-limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.

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