Calculus of Variations and Geometric Measure Theory
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Qualitative properties of critical Dirac equations

William Borrelli (Dipartimento di Matematica e Fisica, Università Cattolica)

created by malchiodi on 27 May 2019

3 jun 2019 -- 14:00   [open in google calendar]

Scuola Normale Superiore, Aula Bianchi

Abstract.

Critical nonlinear Dirac equations appear in problems from Geometric Analysis, like the spinorial Yamabe problem or the immersion of constant mean curvature surfaces, and in Mathematical Physics, as effective 2D models for the wave propagation in graphene and in honeycomb structures. In this talk I will present recent results on the asymptotic behavior of solutions and on their regularity. Such results hold in dimension n greater or equal than two and for a large class of nonlinearities of critical growth. Solutions of a particular form have been classified. In particular, in physically relevant cases in 2D we show that all possible asymptotic behaviors are realized.

This is a joint work with R.L. Frank (LMU Munich & Caltech).

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