Inequalities between Neumann and Dirichlet eigenvalues of Schrödinger operators

  • Jonathan Rohleder

    Stockholm University, Sweden
Inequalities between Neumann and Dirichlet eigenvalues of Schrödinger operators cover
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Abstract

Given a Schrödinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann and Dirichlet boundary conditions, respectively. The obtained inequalities depend partially on monotonicity and convexity properties of the potential. The results are counterparts of classical inequalities for the Laplacian but display some distinction between the one-dimensional case and higher dimensions.

Cite this article

Jonathan Rohleder, Inequalities between Neumann and Dirichlet eigenvalues of Schrödinger operators. J. Spectr. Theory 11 (2021), no. 3, pp. 915–933

DOI 10.4171/JST/361