

201920/
Seminari A.A. 20192020 

I Seminari si svolgono il martedì alle 14:30 nell'aula 311
del Dipartimento di Matematica
(salvo diversa indicazione)



Relatore 
Titolo 
Data 



Christoph Lehner


17 dicembre 2019 



Chiara Boccato
IST Austria 

12 novembre 2019 



Maxime Hauray
Univeristé AixMarseille 

05 novembre 2019 



Nguyen Tong Xuan
GSSI L'Aquila 

28 ottobre 2019 (lunedì) 



Sara Daneri
GSSI L'Aquila 

22 ottobre 2019 



In this talk I will review some recent results obtained in
collaboration with E. Runa and A. Kerschbaum on the onedimensionality
of the minimizers of a family of continuous local/nonlocal interaction
functionals. Such functionals have a local term, typically the
perimeter or its ModicaMortola approximation, which penalizes
interfaces, and a nonlocal term favouring oscillations which are high
in frequency and in amplitude. The competition between the two terms
is expected by experiments and simulations to give rise to periodic
patterns at equilibrium.
Functionals of this type are used to model pattern formation, either
in material science or in biology. The difficulty in proving the
emergence of such structures is due to the fact that the functionals
are symmetric with respect to permutation of coordinates, while
minimizers are not. We will present results showing that for two
classes of functionals (used to model generalized antiferromagnetic
systems, respectively colloidal suspensions), both in sharp interface
and in diffuse interface models, minimizers are onedimensional and
periodic, in general dimension. In the discrete setting such results
had been previously obtained by Giuliani and Seiringer.




Horst Knörrer
ETH Zürich 

15 ottobre 2019 




