Filippo Santambrogio
A Modest Proposal for MFG with Density Constraints.
Fri, 11/04/2011 - 15:01 — SomNambulAuthors: Filippo Santambrogio
Subjects: Analysis of PDEs
AbstractWe consider a typical problem in Mean Field Games: the congestion case, where
in the cost that agents optimize there is a penalization for passing through
zones with high density of agents, in a deterministic framework. This
equilibrium problem is known to be equivalent to the optimization of a global
functional including an $L^p$ norm of the density.A macroscopic crowd motion model of gradient flow type.
Thu, 02/04/2010 - 16:01 — SomNambulAuthors: Filippo Santambrogio, Bertrand Maury, Aude Roudneff-Chupin
Subjects: Analysis of PDEs
AbstractA simple model to handle the flow of people in emergency evacuation
situations is considered: at every point x, the velocity U(x) that individuals
at x would like to realize is given. Yet, the incompressibility constraint
prevents this velocity field to be realized and the actual velocity is the
projection of the desired one onto the set of admissible velocities. Instead of
looking at a microscopic setting (where individuals are represented by rigid
discs), here the macroscopic approach is investigated, where the unknwon is the
evolution of the density .Least Squares estimation of two ordered monotone regression curves.
Tue, 10/20/2009 - 12:53 — SomNambulAuthors: Fadoua Balabdaoui, Filippo Santambrogio, Kaspar Rufibach
Subjects: Methodology
AbstractIn this paper, we consider the problem of finding the Least Squares
estimators of two isotonic regression curves $g^\circ_1$ and $g^\circ_2$ under
the additional constraint that they are ordered; e.g., $g^\circ_1 \le
g^\circ_2$.A Modica-Mortola approximation for branched transport.
Thu, 09/17/2009 - 10:33 — SomNambulAuthors: Filippo Santambrogio
Subjects: Optimization and Control
AbstractThe M^\alpha energy which is usually minimized in branched transport problems
among singular 1-dimensional rectifiable vector measures with prescribed
divergence is approximated (and convergence is proved) by means of a sequence
of elliptic energies, defined on more regular vector fields. The procedure
recalls the Modica-Mortola one for approximating the perimeter, and the
double-well potential is replaced by a concave power.A strategy for non-strictly convex transport costs and the example of ||x-y||p in R2.
Wed, 09/16/2009 - 13:15 — SomNambulAuthors: Filippo Santambrogio, Guillaume Carlier, Luigi De Pascale
Subjects: Classical Analysis and ODEs
AbstractThis paper deals with the existence of optimal transport maps for some
optimal transport problems with a convex but non strictly convex cost. We give
a decomposition strategy to address this issue. As part of our strategy, we
have to treat some transport problems, of independent interest, with a convex
constraint on the displacement.A strategy for non-strictly convex transport costs and the example of ||x-y||p in R2.
Wed, 09/16/2009 - 13:15 — SomNambulAuthors: Filippo Santambrogio, Guillaume Carlier, Luigi De Pascale
Subjects: Classical Analysis and ODEs
AbstractThis paper deals with the existence of optimal transport maps for some
optimal transport problems with a convex but non strictly convex cost. We give
a decomposition strategy to address this issue. As part of our strategy, we
have to treat some transport problems, of independent interest, with a convex
constraint on the displacement.Continuity in two dimensions for a very degenerate elliptic equation.
Wed, 09/16/2009 - 13:15 — SomNambulAuthors: Filippo Santambrogio, Vincenzo Vespri
Subjects: Analysis of PDEs
AbstractAn elliptic equation div(F(Du)) = f whose ellipticity strongly degenerates
for small values of Du (say, F = 0 on B(0,1)) is considered. The aim is to
prove regularity for F(Du). The paper proves a continuity result in dimension
two and presents some applications.
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