[CvGmt News] Seminari Calcolo delle Variazioni

[depascal at dm.unipi.it]

Entropy method for line energies
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   The next CVGMT seminar will be

   Wednesday, march 24 at 5 pm, Sala seminari del Dipartimento di
   Matematica

   Prof. Radu Ignat (Univ. Paris-Sud 11)

   Title: Ëntropy method for line energies"

   Abstract: The aim of this talk is to analyze energy functionals
   concentrated on the jump set of 2D vector fields of unit length and of
   vanishing divergence. The motivation of this study comes from thin-film
   micromagnetics where these functionals correspond to limiting
   wall-energies. The main issue consists in characterizing the
   wall-energy density (the cost function) so that the energy functional
   is lower semicontinuous (l.s.c.). The key point resides in the concept
   of entropies due to the scalar conservation law implied by our vector
   fields. Our main result identifies appropriate cost functions
   associated to certain sets of entropies. In particular, certain power
   cost functions lead to l.s.c. energy functionals. A second issue
   concerns the existence of minimizers of such energy functionals that we
   prove via a compactness result. A natural question is whether the
   viscosity solution is a minimizing configuration. We show that in
   general it is not the case for nonconvex domains. However, the case of
   convex domains is still open. The talk is a joint work with Benoit
   Merlet, Ecole Polytechnique (Paris).


You find this news in the cvgmt preprint server: http://cvgmt.sns.it/news/20100324/