Patterns formation for minimizers of a local/non-local interaction functional in general dimension

The Porous Medium Equation with Large Initial Data on Negatively Curved Riemannian Manifolds

Finite Energy Weak Solutions of the Quantum Navier-Stokes equations

Nonlocal obstacle problems: regularity of the solutions and the free boundaries

Blowup for Fractional NLS

Rademacher’s Theorem, Cheeger’s Conjecture and PDEs for measures

Fractional div-curl quantities and applications to nonlocal geometric equations

Partial Regularity for Holonomic Minimisers of Quasiconvex Functionals

A Morse index formula for the Lane-Emden problem

Variational aspects of Liouville equations and systems on compact surfaces