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Lower bounds for Dirichlet Laplacians and uncertainty principles

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arxiv 1808.04202 v2 pith:ZO5RSTQ4 submitted 2018-08-13 math-ph math.MPmath.SP

Peter Stollmann , Günter Stolz This is my paper · ORCID
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keywords boundsdirichletlowerprinciplesuncertaintyconditionscontinuousderive
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We prove lower bounds for the Dirichlet Laplacian on possibly unbounded domains in terms of natural geometric conditions. This is used to derive uncertainty principles for low energy functions of general elliptic second order divergence form operators with not necessarily continuous main part.

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  1. Sampling and equidistribution theorems for elliptic second order operators, lifting of eigenvalues, and applications

    math.AP 2025-05 conditional novelty 3.0 of 10

    Tautenhahn and Veselic correct an error in their 2020 proof and establish scale-free sampling and equidistribution estimates for eigenfunctions of elliptic second order operators with Lipschitz coefficients.

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