Calculus of Variations and Geometric Measure Theory
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W. Borrelli - R. L. Frank

Sharp decay estimates for critical Dirac equations

created by borrelli on 12 Dec 2018
modified on 09 Mar 2020

[BibTeX]

Published Paper

Inserted: 12 dec 2018
Last Updated: 9 mar 2020

Journal: Trans. Amer. Math. Soc.
Year: 2020
Doi: https://doi.org/10.1090/tran/7958

ArXiv: 1809.01417 PDF

Abstract:

We prove sharp pointwise decay estimates for critical Dirac equations on ℝn with n≥2. They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited states with an explicit asymptotic behavior. Moreover, we provide some classification results both for ground states and for excited states.

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