BOUND ON THE NUMBER OF NEGATIVE EIGENVALUES OF TWO-DIMENSIONAL SCHRODINGER OPERATORS ON DOMAINS

Frank, Rupert L. and Laptev, A. (2019): BOUND ON THE NUMBER OF NEGATIVE EIGENVALUES OF TWO-DIMENSIONAL SCHRODINGER OPERATORS ON DOMAINS. In: St Petersburg Mathematical Journal, Vol. 30, No. 3: pp. 573-589

Abstract

A fundamental result of Solomyak says that the number of negative eigenvalues of a Schriidinger operator on a two-dimensional domain is bounded from above by a constant times a certain Orlicz norm of the potential. Here it is shown that in the case of Dirichlet boundary conditions the constant in this bound can be chosen independently of the domain.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1061-0022
• Language: English