Work

Sharp decay estimates for critical Dirac equations

Year: 2019

Type: article

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.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/7958

Authors: William Borrelli, Rupert L. Frank

Institutions: Scuola Normale Superiore, California Institute of Technology, Ludwig-Maximilians-Universität München

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Analytical Methods in Mathematical Physics