Inequalities involving Aharonov–Bohm magnetic potentials in dimensions 2 and 3

DOI10.1142/S0129055X21500069zbMath1499.81058arXiv1902.06454MaRDI QIDQ5156080

Michael Loss, Denis Bonheure, Maria J. Esteban, Jean Dolbeault, A. A. Laptev

Publication date: 14 October 2021

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.06454

zbMATH Keywords

symmetry breakingcylindrical symmetryoptimal constantsradial symmetrymagnetic Schrödinger operatorAharonov-Bohm magnetic potentialmagnetic Hardy inequalitymagnetic interpolation inequalitymagnetic Keller-Lieb-Thirring inequalitymagnetic rings

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Applications of functional analysis in quantum physics (46N50) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Variational methods for second-order elliptic equations (35J20) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (2)

Improved \(L^p\)-Hardy and \(L^p\)-Rellich inequalities with magnetic fields ⋮ Functional inequalities: nonlinear flows and entropy methods as a tool for obtaining sharp and constructive results

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