The classical Faber-Krahn inequality asserts that balls (uniquely) minimize the first eigenvalue of the Dirichlet-Laplacian among sets with given volume. I will show a sharp quantitative enhancement o...
The limit behaviour of variational systems depending on small parameters (e.g. homogenization, phase transitions, etc.) is often successfully described in terms of Gamma-convergence both in the static...
We show that the combined action of similarity and symmetry produces 2D finite differences (2D dynamics) in the limit of 1D finite differences (1D dynamics). This provides a construction of the 2D Lap...
We consider the evolution of an interface generated between two immiscible, incompressible and irrotational fluids. Specifically we study the Muskat equation (the interface between oil and water in sa...
We present short time existence, uniqueness, and regularity results for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained two-dimensional film...
Baouendi-Grushin operators are important classes of degenerate elliptic operators which are strongly connected with other domains of mathematics such as subriemannian geometry. Parabolic problems asso...
Abstract: It has been known for centuries that a body in contact with a substrate will start to slide only when the lateral force exceeds the static friction force. The transition from static to dynam...
Zubov's method is a technique to characterize the domain of attraction of locally asymptotically stable equilibria of an ordinary differential equation (ODE) as the sublevel set of an appropriate Hami...
Relaxation is a procedure in optimal control problem in which extra elements are added to the domain of an optimization problem in order to guarantee the existence of a minimizer. Of course the relaxe...
We will discuss recent works with Duyckaerts and Merle, dealing with global well posedness, blow-up and soliton resolution, for the energy critical wave equation....
