Estimates for the lowest eigenvalue of magnetic Laplacians

DOI10.1016/j.jmaa.2016.02.073zbMath1386.35295arXiv1501.05554OpenAlexW2963725028MaRDI QIDQ266479

Hynek Kovařík, Fabian Portmann, Tomas Ekholm

Publication date: 13 April 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.05554

zbMATH Keywords

eigenvaluesmagnetic fieldsmagnetic Dirichlet Laplacian

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Estimates of eigenvalues in context of PDEs (35P15) Schrödinger operator, Schrödinger equation (35J10) Variational methods for second-order elliptic equations (35J20)

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Cites Work

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• Sums of magnetic eigenvalues are maximal on rotationally symmetric domains
• Sharp asymptotics for the Neumann Laplacian with variable magnetic field: case of dimension 2
• Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian
• Spectral methods in surface superconductivity
• Semi-classical analysis for the Schrödinger operator and applications
• Schrödinger operators with magnetic fields. I: General interactions
• Lifschitz tail in a magnetic field: The nonclassical regime
• Diamagnetic behavior of sums of Dirichlet eigenvalues
• Elliptic partial differential equations of second order
• Rayleigh-type isoperimetric inequality with a homogeneous magnetic field
• Generalized Hardy inequality for the magnetic Dirichlet forms
• Proof of the fundamental gap conjecture
• Eigenvalue problems of Ginzburg–Landau operator in bounded domains
• Improved Berezin—Li—Yau inequalities with magnetic field
• Magnetic spectral bounds on starlike plane domains
• Stability of the Magnetic Schrödinger Operator in a Waveguide
• Magnetic bottles in connection with superconductivity