## Program

To be announced.

### Invited lectures

#### Michael Bildhauer

##### Some analytical results for image restoration methods of linear growth type

Different linear growth methods for the restoration of images are
discussed. In the first part we concentrate on several variational approaches, which in
the case of appropriate ellipticity conditions lead to regular solutions.
The so called Edge-Enhancing Anisotropic Diffusion used for image compression is studied in the second part of the talk. The underlying integrodifferential operator under consideration is based on the so called Charbonnier
diffusivity w.r.t. a Gaussian kernel which operates across the edge direction.
Here we prove the existence of solutions via fixed point arguments and discuss apriori estimates of suitable iterated sequences.
The results were mainly obtained as joint work with Marcelo Cárdenas, Martin Fuchs and Joachim Weickert.

#### Gilles A. Francfort

##### Regularity and rigidity of the stress field in Von Mises plasticity

In this joint work with J. F. Babadjian, inspired from prior work with A. Giacomini and J. J. Marigo, we start an investigation of spatial hyperbolicity in Von Mises elasto-plasticity, the ultimate goal being an adjudication of the uniqueness of the plastic strain.
After discussing a specific example where uniqueness, or lack thereof, can be established, I will present partial results, focussing on a 2d simplified model.

#### Juha Kinnunen

##### Higher integrability for doubly nonlinear parabolic equations

#### Giuseppe Mingione

##### TBA

#### Domenico Mucci

##### TBA

#### Yasemin Şengül

##### TBA

#### Lenka Slavíková

##### A sharp boundedness criterion for bilinear Fourier multipliers

A linear Fourier multiplier operator associated with an arbitrary bounded function is always \(L^2\)-bounded. The related question of the \(L^2\times L^2 \to L^1\) boundedness of bilinear Fourier multiplier operators is however much less straightforward; in particular, there are bounded functions for which the associated bilinear operator is unbounded from \(L^2 \times L^2\) to \(L^1\). In this talk we present a sharp criterion for the \(L^2 \times L^2 \to L^1\) boundedness of bilinear Fourier multipliers. This is a joint work with Loukas Grafakos and Danqing He.

#### Barbara Zwicknagl

##### TBA

#### Cristiana De Filippis

##### TBA