Optimal measures for the fundamental gap of Schrödinger operators
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 1, p. 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 : https://doi.org/10.1051/cocv:2008069
Classification:  35J10,  49K20,  35J20,  35B20
Keywords: Schrödinger operator, eigenvalue problems, measure theory, shape optimization
@article{COCV_2010__16_1_194_0,
author = {Varchon, Nicolas},
title = {Optimal measures for the fundamental gap of Schr\"odinger operators},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {16},
number = {1},
year = {2010},
pages = {194-205},
doi = {10.1051/cocv:2008069},
zbl = {1183.35092},
mrnumber = {2598095},
language = {en},
url = {http://www.numdam.org/item/COCV_2010__16_1_194_0}
}

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://www.numdam.org/item/COCV_2010__16_1_194_0/

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