[CvGmt News] [CVGMT] weekly bulletin

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Weekly bulletin of http://cvgmt.sns.it

--- Summary ---
* Seminars by: Martinazzi, Muratov
* New papers by: Santambrogio, Radici, Zeppieri, Mészáros, Bevan, Cardaliaguet* Modified papers by: Shahgholian, Louet, Ambrosio, Brasco, Santambrogio, Rizzi, Ruffini, Marini, Velichkov, De Pascale, De Philippis, Silva, Mészáros, Crippa, Figalli, Barilari, Agrachev
--- Seminars next week ---
* Tuesday 14 jul 2015

time: 16:00
Scuola Normale Superiore,  Aula Bianchi Scienze
The fractional Liouville equation in   dimension 1 - Compactness and  quantization
Luca Martinazzi (University of Basel)
Abstract. In this talk I will introduce the fractional Liouville equation on the circle S1 and its geometric interpretation in terms of conformal immersions of the unit disk into the complex plane. Using this interpretation we can show that the solution of the fractional Liouville equation have very precise compactness properties (including quantization) with a clear geometric counterpart. I will also compare these result with analogue ones for the classical Liouville equation in dimension 2, used to prescribe the Gaussian curvature.

This is a joint work with Tristan Riviere and Francesca Da Lio.

* Wednesday 15 jul 2015

time: 16:00
Dipartimento di Matematica, Sala Seminari
A non-local variational problem arising from studies of nonlinear charge screening in graphene monolayers
Cyrill Muratov 
Abstract. This talk is concerned with energy minimizers in an orbital-free density
functional theory that models the response of massless fermions in a
graphene monolayer to an out-of-plane external charge. The considered energy
functional generalizes the Thomas-Fermi energy for the charge carriers in
graphene layers by incorporating a von-Weizsaecker-like term that penalizes
gradients of the charge density. Contrary to the conventional theory,
however, the presence of the Dirac cone in the energy spectrum implies that
this term should involve a fractional Sobolev norm of the square root of the
charge density. We formulate a variational setting in which the proposed
energy functional admits minimizers in the presence of an out-of-plane point
charge. The associated Euler- Lagrange equation for the charge density is
also obtained, and uniqueness, regularity and decay of the minimizers are
proved under general conditions. In addition, a bifurcation from zero to
non-zero response at a finite threshold value of the external charge is
proved. This is joint work with J. Lu and V. Moroz.

--- New Papers ---
* Radici: A planar Sobolev extension theorem for piecewise linear homeomorphisms
* Bevan, Zeppieri: A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation
* Cardaliaguet, Mészáros, Santambrogio: First order Mean Field Games with density constraints: Pressure equals Price
--- Modified Papers ---
* Agrachev, Barilari, Rizzi: Curvature: a variational approach 
* Ambrosio, Crippa: Continuity equations and ODE flows with non-smooth velocity
* Marini, Ruffini: On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization
* De Pascale, Louet, Santambrogio: The Monge problem with vanishing gradient penalization: vortices and asymptotical profile
* De Philippis, Mészáros, Santambrogio, Velichkov: BV estimates in optimal transportation and applications
* Figalli, Shahgholian: An overview of unconstrained free boundary problems
* Mészáros, Silva: A variational approach to second order mean field games with density constraints: the stationary case
* Brasco, Ruffini: Compact Sobolev embeddings and torsion functions
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