Mathematical remarks on the optimized effective potential problem. (English) Zbl 1224.35102

Ben-Haj-Yedder, Adel; Cances, Eric; Le Bris, Claude

Differ. Integral Equ. 17, No. 3-4, 331-368 (2004).

Optimal effective potential (OEP) problem—minimization problem from computational chemistry is analyzed. In order to obtain rigorous results, several assumptions substantially constraining the original OEP problem are made. (For example molecular system with only two electrons is considered etc.) As a result, only somewhat academic cases are studied, laying, however, rigorous foundations for further more general works.
A weak formulation of the (simplified) OEP problem is presented and it is shown to be well posed. Various related problems are also analyzed.

Reviewer: Vojtěch Pravda (Praha)

MSC:

35J50	Variational methods for elliptic systems
35Q40	PDEs in connection with quantum mechanics

Keywords:

optimal effective potential problem; minimization problem; well-posedness