Sharp decay estimates for critical  Dirac equations

Borrelli, William; Frank, Rupert

doi:10.1090/tran/7958

Sharp decay estimates for critical Dirac equations
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by William Borrelli and Rupert L. Frank PDF

Trans. Amer. Math. Soc. 373 (2020), 2045-2070

Abstract:

We prove sharp pointwise decay estimates for critical Dirac equations on $\mathbb {R}^n$ with $n\geqslant 2$. 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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