Seminar

Variational methods for hyperbolic obstacle-type problems, k-harmonic maps with defects and optimal Steiner-type networks

Cycle 34th Oral Defence of the Phd Thesis
28 January 2022
Online
Organizer: 
Doctoral School in Mathematics
Target audience: 
University community
Attendance: 
Online – Registration required
Registration email: 
Contact person: 
Orlandi Giandomenico

Venue: The event will take in presence only for the Phd student and part of the commission and online through the ZOOM platform. To get the access codes please contact the secretary office (phd.maths [at] unitn.it)
Time:10:00 a.m.

Van Phu Cuong Le - PhD in Mathematics, University of Trento

Abstract:
In this final seminar, we will first present existence results for a class of hyperbolic obstacle-type problems by using a variational approach in the spirit of minimizing movements. We consider both linear and nonlinear cases, as well as non-local (fractional) operators. We discuss some applications to singular limits of nonlinear wave equations and to nonlinear waves in adhesive phenomena. Then, we move to discuss the relation between energy minimizing maps with prescribed singularities and (Gilbert-)Steiner optimal transport networks. More precisely, we show the equivalence of the corresponding variational problems, interpreting in particular the branched optimal transport problem as a homological Plateau problem for rectifiable currents with values in a suitable normed group. This generalizes the pioneering work by Brezis, Coron and Lieb.

Supervisor: Giandomenico Orlandi