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Frank, R. 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

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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.

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