I will introduce a new heat flow for harmonic maps with free boundary. After giving some motivations to study such maps in relation with extremal metrics in spectral geometry, I will construct weak so...
Interfacial energy functionals are ubiquitous in nature. However, some of the most basic questions are still open. In this talk, I will address one of these questions and characterize local minimizers...
I will survey on some long-standing open problems and some recent results about the regularity of minimizers of various relaxed energies. I will focus on the model case of harmonic maps from the 3-dim...
Il moto per curvatura media a volume costante è l'evoluzione di una ipersuperficie con velocità data dalla curvatura media, con un termine aggiuntivo non locale tale che il volume racchiuso resti cost...
n this talk we present some results obtained jointly with Matteo Muratori (Politecnico di Milano), focusing on qualitative properties for • Extremals for the Sobolev inequality, • Positive radial solu...
La convergenza in tempo lungo per equazioni di Fokker-Planck con drift confinante è un tema classico, affrontato finora sia con metodi variazionali che probabilistici. Nel seminario discuterò un nuovo...
We study the evolution in time of smooth sets in the n–dimensional flat torus, such that their boundaries, which are smooth hypersurfaces, move by surface diffusion flow (i.e. the H−1H−1 gradient flow...
The regularity of solutions of the Dirichlet problem for the Laplace operator in corner domains is limited by the existence of harmonic functions that are zero on the boundary of some tangent cones. T...
On non-smooth domains, elliptic regularity for solutions of boundary value problems, measured by Sobolev norms, will only hold for a restricted set of regularity indices, due to singularities of the s...
When minimizing a regularized functional - i.e., one of the form \(H(u) = F(u) + \alpha G(u)\), where \(G\) is a regularization term and \(\alpha\) is the regularization parameter - one generally expe...
