Seminars take place in the seminar room, second floor of the building Le Chablais, on the Bourget-du-lac (Savoy) site.

## Next seminar:

**Friday 24th November 2017 at 10h
**
Antonio Leaci
(Università del Salento),
*Image segmentation and inpainting by variational methods.*

Abstract:(Hide abstracts)

The aim of the talk is to provide a concise survey of some results about variational methods for image segmentation and inpainting, in the framework of functions of Special Bounded Variation in the sense of De Giorgi.

The seminar of the team EDPs² is under the responsibility of Jimmy Garnier.

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Other years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017,
all years together.

# Year 2018

**Friday 12th January 2018 at 14h
**
Journée Calcul des Variations et EDP
(Université Grenoble),
*Journée Calcul des Variations et EDP, le 12 Janvier 2018 à Grenoble*

**Friday 12th January 2018 at 14h
**
Anne de Bouard
(Ecole Polytechnique),
*à venir*

**Thursday 25th January 2018 at 14h
**
Gilles Lebeau
(Univ Nice Sophia-Antipolis),
*à venir*

**Friday 26th January 2018 at 13h30
**
Gianluca Crippa
(University of Basel),
*Eulerian and Lagrangian solutions of the continuity equation*

Abstract:(Hide abstracts)

It is well known that the motion of an incompressible fluid can be described in Eulerian variables (as a solution of a PDE, namely the continuity equation), or alternatively in Lagrangian variables (as a flow of an ODE). The classical DiPerna-Lions-Ambrosio theory ensures well-posedness and provides structural properties for solutions of the continuity equation, under suitable regularity assumptions on the velocity field and integrability assumptions on the solution. In my talk I will focus on the ``Lagrangianity'' of solutions, that is, on the property of being transported by an ODE flow, hence addressing the question whether an Eulerian solution is automatically a Lagrangian solution. After a brief summary of the DiPerna-Lions-Ambrosio theory, I will present two examples which are outside of the assumptions of such a theory, and in which nevertheless we can prove the Lagrangianity of solutions. The first one concerns vanishing viscosity solutions of the two-dimensional Euler equations, where we can use suitable duality methods (joint work with Stefano Spirito). The second example involves general continuity equations, and requires the proof of a new Lipschitz extension lemma (joint work with Laura Caravenna).

**Friday 9th February 2018 at 14h
**
Michiel Van den Berg
(University Bristol),
*à venir*

**Friday 2nd March 2018 at 14h
**
Tatsuo Iguchi
(Keio University),
*à venir*

The seminar of the team EDPs² is under the responsibility of Jimmy Garnier.

**Settings:**
See
with decreasing date.
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Other years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017,
all years together.