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.
Mots clés : 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}, pages = {194--205}, publisher = {EDP-Sciences}, volume = {16}, number = {1}, year = {2010}, doi = {10.1051/cocv:2008069}, mrnumber = {2598095}, zbl = {1183.35092}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2008069/} }
TY - JOUR AU - Varchon, Nicolas TI - Optimal measures for the fundamental gap of Schrödinger operators JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 194 EP - 205 VL - 16 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008069/ DO - 10.1051/cocv:2008069 LA - en ID - COCV_2010__16_1_194_0 ER -
%0 Journal Article %A Varchon, Nicolas %T Optimal measures for the fundamental gap of Schrödinger operators %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 194-205 %V 16 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008069/ %R 10.1051/cocv:2008069 %G en %F COCV_2010__16_1_194_0
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. http://archive.numdam.org/articles/10.1051/cocv:2008069/
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