Differential equations

The group works on the mathematical analysis of nonlinear partial differential equations and their applications, with two main and closely related research lines.

The first line studies elliptic equations and variational problems with nonstandard growth, both local and nonlocal. The focus is on quasilinear operators —such as the p-Laplacian and its generalizations in Orlicz–Sobolev spaces— and on nonlocal operators of fractional type, including the fractional g-Laplacian. Problems addressed include existence and regularity of solutions, eigenvalue theory for quasilinear operators, shape optimization, and homogenization.

The second line deals with optimal control and controllability of nonlinear evolution equations, in particular Schrödinger-type equations and systems modeling nematic liquid crystals. Within this framework, the propagation of optical solitons is studied and numerical methods for their simulation are developed.

Cutting across both lines, the group develops mathematical models with applications in biology and the social sciences. This includes the design and analysis of optimal control strategies for epidemic models (of SIR type), models of opinion formation and political polarization in large populations —approached via kinetic and mean-field equations—, evolutionary game theory, and cell signaling dynamics.