[CvGmt News] Seminari Calcolo delle Variazioni
depascal at dm.unipi.it
depascal at dm.unipi.it
Wed Mar 24 10:21:21 CET 2010
This is a memorandum for the talk of this afternoon.
Luigi
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/
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