Calculus of Variations and Geometric Measure Theory
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W. Borrelli

Weakly localized states for nonlinear Dirac equations

created by borrelli on 16 Feb 2018
modified on 03 Oct 2018


Published Paper

Inserted: 16 feb 2018
Last Updated: 3 oct 2018

Journal: Calc. Var. Partial Differential Equations
Year: 2018

ArXiv: 1802.05617 PDF


We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures. We give a direct existence proof thanks to a particular radial ansatz, which also allows to provide the exact asymptotic behavior of spinor components. Moreover, those solutions admit a variational characterization. We also indicate how the content of the present paper allows to extend our previous results for the massive case to more general nonlinearities.

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