An eigenvalue variation problem of magnetic Schrödinger operator in three dimensions (Q1030545)

This paper deals with several problems related to the Schrödinger operator in \({\mathbb R}^3\) with a magnetic potential. One of the main questions studied in the present paper concerns the lowest eigenvalue of the Schrödinger operator. This variational problem is strongly related with a question in the mathematical theory of the surface smectic state of liquid crystals. The main result of the paper establishes both an upper bound and a lower bound of the the lowest eigenvalue of the Schrödinger operator. The proof strongly relies on the Helffer-Morame techniques, combined with related estimates.