In this seminar we will illustrate a work in collaboration with Ariela Briani and Hitoshi Ishii that extents the well known result on thin domains of Hale and Raugel. The test function approach of C. ...
Diffusion of knowledge models in macroeconomics describe the evolution of an interacting system of agents who perform individual Brownian motions (this is internal innovation) but also can jump on top...
Dynamic boundary conditions play an essential role in acurately modeling complex physical interactions on the boundary. In this lecture we explain the role of dynamic boundary conditions in modeling d...
Think of \begin{center} \( u_{tt} + 2au_t + Au = 0 \) \end{center} as a wave equation. Bounded solutions of this equation tend to solutions of the heat equation \begin{center} \( 2av_t + Av = 0. \) \e...
In this talk we describe the influence of the initial data and the forcing terms on the regularity of the solutions to a class of evolution equations including the heat equation, linear and semilinear...
Suppose that two nonlocal minimal surfaces are included one into the other and touch at a point. Then, they must coincide. But this is perhaps less obvious than what it seems at first glance. This se...
We present a new Mountain Pass Theorem for a class of functionals that depends on two arguments which only partially satisfies the Palais-Smale condition. This abstract functional setup will be a...
We will introduce and discuss a notion of s-fractional mass for 1-currents, generalizing the s-fractional perimeter in the plane to higher codimension singularities. We will present basic compactn...
I will first present a convergence result for solutions of Allen-Cahn type systems with a multiple-well potential involving the usual fractional Laplacian in the regime of the so-called nonlocal mini...
We present a survey of nonlinear elliptic equations with nonlocal interactions. These equations describe the collective behavior of self-interacting many-body systems at different scales, from atoms a...
