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Abstract: Let Ω be a bounded convex domain in Euclidean space R^n. Consider the Schrödinger operator -Δ+V for a nonnegative convex potential V on Ω under Dirichlet boundary conditions. Under these assumptions the eigenvalues are discrete and satisfy 0 < 3; : : : . When the potential is identically zero we will just write i; for these eigenvalues. The quantity is called the spectral gap. It was conjectured by M. van den Berg [4] that can be estimated below by 3 where d... (Update)
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BibTeX entry: (Update)
@misc{ banuelos-gradient,
author = "Rodrigo Ba{\~n}uelos and Pawel Kr{\"o}ger",
title = "Gradient Estimates for the Ground State {Schr\"o}dinger Eigenfunction and Applications",
url = "citeseer.ist.psu.edu/621495.html" }
Citations (may not include all citations):22 On extensions of the Brunn-Minkowski and Prekopa-Leindler t.. (context) - Brascamp, Lieb - 1976
2 Optimal lower bounds for eigenvalue gaps for Schodinger ope.. (context) - Ashbaugh, Benguria - 1988
2 the spectral gap of the Dirichlet Laplacian (context) - Davis
1 boson gas and the spectrum of the laplacian (context) - van den Berg - 1983
1 Sharp inequalities for heat kernels of Schrodinger operator.. (context) - nuelos, endez-Hern - 2000
1 Optimal lower bounds for the gap between the rst two eigenva.. (context) - Ashbaugh, Benguria - 1989
1 An extension of a theorem by Brascamp and Lieb (context) - oger - 2000
1 A lower bound for the gap between the rst two eigenvalues of.. (context) - Lin
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