## My interest fields in Mathematics

- Study of the contact angle at the junction of an interface and a rough wall (Mathematical study of the possibility of describing hysteresis phenomenon) collaboration with G. Bouchitté.
- Study of tude an asymptotic model for desribing line tension : an energy localized at the junction of an interface and a wall. Collaboration with G. Bouchitté and G. Alberti (Pisa, Italy).
- Relaxation of energies partially localized on low dimensional structures. Collaboration with G. Buttazzo (Pisa Italy) and
G. Bouchitté.
- Study of shapes obtained through topological optimization : a theoritical study in collaboration with G. Buttazzo and G. Bouchitté and a numerical study in collaboration avec F. Golay,
- Homogeneization of an elastic material containing a network of elastic beams. We show that we can obtain a material of a very new kind.
- A singular perturbation problem with a potential which degenerates at infinity. Application to the modelisation of a cloud of small droplets. Application to image segmentation.
- Study of the closure of the set of diffusion functionnals. We show that any Dirichlet form is the limit of some sequence of diffusion functionnal. An homogenization result with a specific non local behavior at the limit is an interesting intermediate result.
- Homogenization of pantographic_type trusses.Convergence to one-dimensionnal models the energy of which depend on the strain gradient or on its second gradient.
- Determination of the closure of the set of elasticity functionnals. We show that it is made of all lower semi continuous, objective quadratic forms.
- Transport optimization with concave cost. We check if this leads to a well posed problem under the constraint of a one dimensionnal transport and if it can be regularized by means of a potential degenerated at infinity.
à l'infini.
- Developpement with Matlab/Octave of a software for optimizing chemical constants in order to interpret series of experimental results.
- Variationnal study of non-planar elastic rods.
collaboration with C. Pideri. We obtain an asymptotic bound for the Korn constant in a tubular neighborhood of a non planar curve as its radius tends to zero. The results are extended in the case of non linear elasticity, owing the the rigidity lemma of James, Friesecke,
Muller. The limit model for a non planar elastic beam with large displacements is obtained.