Sharp inequalities for heat kernels of Schrödinger operators and applications to spectral gaps

DOI10.1006/jfan.2000.3611zbMath0966.35090OpenAlexW2091850287MaRDI QIDQ1585978

Rodrigo Bañuelos, Pedro J. Mendez-Hernandez

Publication date: 16 August 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/0eb9221018b5b941bc727ab2dfc4e0c15931b649

zbMATH Keywords

spectral gaprearrangement inequalitiesdifference of the first two eigenvalues

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Schrödinger operator, Schrödinger equation (35J10)

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Cites Work

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• On the second eigenfunctions of the Laplacian in \({\mathbb{R}}^ 2\)
• Symmetry and related properties via the maximum principle
• On the ``hot spots conjecture of J. Rauch
• A lower bound for the gap between the first two eigenvalues of Schrödinger operators on convex domains in \(\mathbb{S}^ n\) or \(\mathbb{R}^ n\)
• A general rearrangement inequality for multiple integrals
• Spectral gaps and rates to equilibrium for diffusions in convex domains
• On two conjectures in the fixed membrane eigenvalue problem
• Remarks on the Second Eigenvalue of a Symmetric Simply Connected Plane Region
• Lower Bounds of the Gap Between the First and Second Eigenvalues of the Schrodinger Operator
• A Counterexample to the Nodal Domain Conjecture and a Related Semilinear Equation
• Optimal Lower Bound for the Gap Between the First Two Eigenvalues of One-Dimensional Schrodinger Operators with Symmetric Single-Well Potentials
• Lower bound gradient estimates for solutions of schrodinger equations and heat kernels
• The Eigenvalue Gap for One-Dimensional Convex Potentials