In a recent paper, we study the long--time behavior and the stability of the surface diffusion flow of smooth hypersurfaces in the flat torus \(\mathbb T^n\). According to this flow, smooth hypersurfa...
The classical Courant's nodal domain theorem states that the n-th eigenfunction of the Laplacian on a compact manifold has at most n nodal domains. The same holds for Steklov eigenfunctions on a compa...
In this talk I will present some recent results on the Kirchhoff equation of nonlinear elasticity, describing transversal oscillations of strings and plates, with periodic boundary conditions. We are...
We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actua...
I shall consider elliptic problems addressing the study of the geometric properties of the solutions. This issue is in general related to the classification of the solutions or to Liouville type theor...
In this talk we consider inverse problems for the partial differential equations describing the behavior of certain fluids. Our focus will be on the fluid-structure interaction problem and the object...
We study some qualitative properties of the solutions to a segregation limit problem in planar domains. The main goal is to show that, generically, the limit configuration of N competing populations c...
On several types of fractals, it is possible to build a Dirichlet form in a natural way; it is also possible to define a dynamical system and we shall see that the Dirichlet form has a natural relatio...
I present some results concerning the number of critical points and the number of nodal domains of Steklov eigenfunctions. The results have been obtained in collaboration with Luca Battaglia (Roma 3),...
We consider radial solutions of fully nonlinear, uniformly elliptic equations posed in punctured balls, in presence of radial singular quadratic potentials. We discuss both the principal eigenvalues p...
