Bound on the number of negative eigenvalues of two-dimensional Schr\"odinger operators on domains

R. L. Frank ; A. Laptev

Algebra i analiz, Tome 30 (2018) no. 3, pp. 250-272.

Résumé

A fundamental result of Solomyak says that the number of negative eigenvalues of a Schrödinger 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.

Détail

Keywords: Schrödinger operator, Dirichlet Laplacian, Neumann Laplacian, Trudinger inequality.

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