Optimal measures for the fundamental gap of Schrödinger operators
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 1, pp. 194-205.

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 L1 constraints.

DOI: 10.1051/cocv:2008069
Classification: 35J10, 49K20, 35J20, 35B20
Keywords: Schrödinger operator, eigenvalue problems, measure theory, shape optimization
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     title = {Optimal measures for the fundamental gap of {Schr\"odinger} operators},
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     pages = {194--205},
     publisher = {EDP-Sciences},
     volume = {16},
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     year = {2010},
     doi = {10.1051/cocv:2008069},
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     url = {http://archive.numdam.org/articles/10.1051/cocv:2008069/}
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Varchon, Nicolas. Optimal measures for the fundamental gap of Schrödinger operators. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 1, pp. 194-205. doi : 10.1051/cocv:2008069. http://archive.numdam.org/articles/10.1051/cocv:2008069/

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