We prove sharp pointwise decay estimates for critical Dirac equations on $ mathbb{R}^n$ with $ ngeq 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.
Borrelli, W., Frank, R. L., Sharp decay estimates for critical Dirac equations, <<TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY>>, 2020; 373 (3): 2045-2070. [doi:10.1090/tran/7958] [http://hdl.handle.net/10807/171304]
Sharp decay estimates for critical Dirac equations
Borrelli, William;
2019
Abstract
We prove sharp pointwise decay estimates for critical Dirac equations on $ mathbb{R}^n$ with $ ngeq 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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