Inequalities between Neumann and Dirichlet eigenvalues of Schr\"odinger operators

16 Mar 2020  ·  Rohleder Jonathan ·

Given a Schr\"odinger 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. read more

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Spectral Theory Mathematical Physics Analysis of PDEs Mathematical Physics