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

2017/12/08 by Rupert L. Frank, Frank, Rupert L., Ари Лаптев +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1712.03167

openalex publication_date 2017/12/08 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

A fundamental result of Solomyak says that the number of negative eigenvalues\nof a Schr "odinger operator on a two-dimensional domain is bounded from above\nby a constant times a certain Orlicz norm of the potential. Here we show that\nin the case of Dirichlet boundary conditions the constant in this bound can be\nchosen independently of the domain.\n

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