Sharp exponential decay for solutions of the stationary perturbed Dirac equation

DOI10.1142/S0219199720500789zbMath1491.35370arXiv1803.00603OpenAlexW3092268100WikidataQ115523113 ScholiaQ115523113MaRDI QIDQ5065093

Biagio Cassano

Publication date: 18 March 2022

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.00603

zbMATH Keywords

Dirac operatorunique continuationlocalization of solutionsnon-Hermitian perturbations

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Perturbations in context of PDEs (35B20) Continuation and prolongation of solutions to PDEs (35B60) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (2)

Symmetric solutions for a 2D critical Dirac equation ⋮ On the Landis conjecture for the fractional Schrödinger equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hardy uncertainty principle and unique continuation properties of covariant Schrödinger flows
• Hardy uncertainty principle, convexity and parabolic evolutions
• The sharp Hardy uncertainty principle for Schrödinger evolutions
• Unique continuation for Schrödinger evolutions, with applications to profiles of concentration and traveling waves
• On spectral stability of the nonlinear Dirac equation
• Carleman estimates and inverse problems for Dirac operators
• Carleman inequalities for the Dirac and Laplace operators and unique continuation
• On the point spectrum of Dirac operators
• Some remarks concerning unique continuation for the Dirac operator
• Self-adjoint extensions for the Dirac operator with Coulomb-type spherically symmetric potentials
• Weakly localized states for nonlinear Dirac equations
• Quantitative uniqueness estimates for the general second order elliptic equations
• A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
• Landis' conjecture for general second order elliptic equations with singular lower order terms in the plane
• A Meshkov-type construction for the borderline case.
• Gaussian decay of harmonic oscillators and related models
• On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials
• On localization in the continuous Anderson-Bernoulli model in higher dimension
• Some Quantitative Unique Continuation Results for Eigenfunctions of the Magnetic Schrödinger Operator
• L²-lower bounds to solutions of one-body Schrödinger equations
• Hardy-Carleman type inequalities for Dirac operators
• Nodal Sets for Eigenfunctions of the Laplacian On Surfaces
• ABSENCE OF EMBEDDED EIGENVALUES OF THE DIRAC EQUATION FOR LONG RANGE POTENTIALS
• Non-existence of eigenvalues of Dirac operators
• ON THE POSSIBLE RATE OF DECAY AT INFINITY OF SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
• Unique continuation and the cauchy problem for first order systems of partial differential equations
• Unique continuation at infinity of solutions to Schrödinger equations with complex-valued potentials
• Uniqueness properties of solutions to Schrödinger equations
• Sharp decay estimates for critical Dirac equations
• On Landis’ Conjecture in the Plane
• The Landis conjecture for variable coefficient second-order elliptic PDEs
• Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations
• Sharp Hardy uncertainty principle and gaussian profiles of covariant Schrödinger evolutions
• Riemannian geometry and geometric analysis

This page was built for publication: Sharp exponential decay for solutions of the stationary perturbed Dirac equation