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Local smoothing estimates for the massless Dirac-Coulomb equation in 2 and 3 dimensions

Cacciafesta, Federico; Séré, Eric (2016), Local smoothing estimates for the massless Dirac-Coulomb equation in 2 and 3 dimensions, Journal of Functional Analysis, 271, 8, p. 2339-2358. 10.1016/j.jfa.2016.04.003

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Type
Article accepté pour publication ou publié
Date
2016
Journal name
Journal of Functional Analysis
Volume
271
Number
8
Publisher
Elsevier
Pages
2339-2358
Publication identifier
Metadata
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Author(s)
Cacciafesta, Federico
Universita degli Studi di Roma
Séré, Eric
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We prove local smoothing estimates for the massless Dirac equation with a Coulomb potential in 2 and 3 space dimensions. Our strategy of proof is inspired by a paper of Burq et al. (2003) about Schroedinger and wave equations with inverse-square potentials, and relies on partial wave subspaces decomposition and spectral analysis of the Dirac-Coulomb operator.
Subjects / Keywords
massless Dirac equation; Dirac-Coulomb; graphene; relativistic quantum mechanics; smoothing estimates; dispersive estimates