no. 1
Optimal measures for the fundamental gap of Schrödinger operators
ESAIM: Control, Optimisation and Calculus of Variations, Tome 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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     author = {Varchon, Nicolas},
     title = {Optimal measures for the fundamental gap of {Schr\"odinger} operators},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {194--205},
     year = {2010},
     publisher = {EDP Sciences},
     volume = {16},
     number = {1},
     doi = {10.1051/cocv:2008069},
     mrnumber = {2598095},
     zbl = {1183.35092},
     language = {en},
     url = {https://www.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, Tome 16 (2010) no. 1, pp. 194-205. doi: 10.1051/cocv:2008069

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