Calculus of Variations and Geometric Measure Theory
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Variational methods and applications

The lifting problem for manifold-valued maps of bounded variation

Giacomo Canevari (Dip. Informatica, Università degli Studi di Verona)

created by paolini on 08 Sep 2021

7 sep 2021 -- 16:00   [open in google calendar]

Abstract.

Let N be a compact, connected, smooth manifold without boundary, embedded in a Euclidean space. Then, any BV-map from a Euclidean domain to N has a BV-lifting to the universal covering of N. In this talk, we will focus on two particular cases: the case N is the circle, and the case N is the real projective plane. These cases arise from variational models in materials science - respectively, the Ginzburg-Landau theory for superconductivity and the Landau-de Gennes model for uniaxial nematic liquid crystals. We will review classical results on the existence of liftings in BV, present some new ones and, if time permits, discuss the structure of liftings in BV. The talk is based on joint work with Giandomenico Orlandi (University of Verona).

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