Recent preprints/publications of Antonin Chambolle
- Optimization for imaging:
- Other imaging applications and variational problems:
- with Thomas Pock, we have just finished
a preprint on a
Roto-translational variation" which extends to arbitrary
images curvature dependent functionals of level sets such as the
Elastica, initially proposed for "inpainting" applications.
- With Benoit Merlet (U. Lille) and Luca Ferrari (CMAP),
we are studying the phase-field approximation of Steiner
type (or mass transportation)
problems. A first result in 2D is found in
A phase-field approximation of the Steiner problem in dimension two
. The general case is treated in Variational approximation of size-mass energies for k-dimensional currents.
- With Vincent Duval (Telecom), Gabriel Peyré (ENS)
and Clarice Poon (U. Cambridge), we have studied some
geometric properties of the total variation denoising, for
simple functions with small noise, in
Total Variation Denoising and Support Localization
of the Gradient
Regularity for the Optimal Compliance Problem with
Length Penalization we have described, with Jimmy
Lamboley, Antoine Lemenant and Eugene Stepanov, the structure
of 1D compact connected sets minimizing some "compliance"
- Analysis of Brittle Fracture.
- With Sergio Conti (U. Bonn) and Gilles Francfort (U. Paris-Nord),
we have proved a Korn-Poincaré inequality for SBD
functions) which show
that if their jump set is small enough, then they satisfy a
classical Korn-Poincaré inequality, up to a small set,
"Korn-Poincare inequalities for functions with a
small jump set" (Indiana U.~Math Journal).
As an application, we are able to show the Gamma-convergence
of fracture models with non-interpenetration, in 2D, cf
of a Brittle Fracture Energy with a Constraint of
- With Vito Crismale (CMAP), we have studied extensively
the "Griffith problem" for the modeling of fracture growth and
have shown existence of solutions, including strong solutions with
a Dirichlet boundary conditions, in two papers
Compactness and lower-semicontinuity in GSBD
(J. Eur. Math. Soc, to appear) and Existence of strong solutions to the Dirichlet problem for the Griffith energy (Cal. Var PDE).
- Together with Flaviana Iurlano (U. Paris 6) and Sergio Conti,
we have succeeded in proving the "GSBD" (brittle fracture
/ Griffith's energy) variant of
De Giorgi, Carriero and Leaci's
result on the Mumford-Shah
Approximation of functions with small jump sets and existence of
strong minimizers of Griffith's energy (JMPA).
- Nonlocal and Crystalline curvature flows:
Quite older publications can be found here.