Research lines

Aggregation-Diffusion Problems

Problems related to the aggregation diffusion equation

\begin{equation} \tag{ADE} \partial_t \rho = \mathrm{div} \Big( \rho \nabla (U’ (\rho) + V + W* \rho) \Big) \end{equation}

Nonlocal Problems

Problems related to fractional Laplacians in the linear and non-linear settings and related topics (existence, regularity, fractional Sobolev spaces, numerical analysis…).

Symmetrisation and rearrangement

We aim to obtain a priori estimates of elliptic and parabolic problems by exploiting the properties of the symmetric decreasing rearrangement either in all variable (Schwarz rearrangement) or some (Steiner rearrangement).

Homogenisation

Problems related mainly to domains with perforated domains.