Optimal measures for the fundamental gap of Schrödinger operators
Collège Condorcet de Bresles, Rue du Petit Chantilly,
60510 Bresles, France. email@example.com
Revised: 24 June 2008
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.
Mathematics Subject Classification: 35J10 / 49K20 / 35J20 / 35B20
Key words: Schrödinger operator / eigenvalue problems / measure theory / shape optimization
© EDP Sciences, SMAI, 2008