Inequalities between Neumann and Dirichlet eigenvalues of Schrödinger operators

2019/07/04 by Rohleder, Jonathan · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1907.02316

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.

Cited by

• The Levine--Weinberger and Friedlander--Filonov inequalities for some classes of elliptic operators

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