R. L. Frank, A. Laptev, “Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains”, Algebra i Analiz, 2018, Volume 30, Issue 3,Pages <nobr>250

This article is cited in 4 papers

Research Papers

Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains

R. L. Frank^ab, A. Laptev^cd

^a Mathematisches Institut, Ludwig-Maximilans Universität München, Theresienstr. 39, 80333, München, Germany
^b Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
^c Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK
^d Institut Mittag-Leffler, Auravägen 17, 182 60, Djursholm, Sweden

Abstract: 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.

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

Received: 08.12.2017

Language: English