We study a system of nonlocal aggregation cross-diffusion PDEs that describe the evolution of opinion densities on a network. The PDEs are coupled with a system of ODEs that describe the time evolutio...
We discuss regularity for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we prove an epsilon-regulari...
Over the last few decades, the study of the nonlinear Schrödinger equation on \(\mathbb{R}^N\) has been investigated by numerous researchers. However, very few results are known when the domain is non...
Nel 2007 Choe-Ghomi and Ritoré hanno provato una disuguaglianza isoperimetrica che afferma che a parità di volume, il minimo del perimetro relativo di un insieme E fuori di un convesso C si realizza q...
The cutoff phenomenon is a now classical topic in probability, that consists in proving an abrupt convergence to equilibrium for a sequence of Markovian dynamics. Classical examples include card shuff...
This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.We consider solutions to some semilinear ell...
Abstract: Optimal transport tools have been extremely powerful to study Ricci curvature, in particular Ricci lower bounds in the non-smooth setting of metric measure spaces (which can be been as a non...
Abstract: The seminar concerns the study of evolution equations on graphs, motivated by applications in data science and opinion dynamics. We will discuss graph analogues of the continuum nonlocal-int...
Abstract: The Lott-Sturm-Villani theory of CD(K, N) metric measure spaces satisfying Ricci curvature lower bounds in a synthetic sense via optimal transport, though extremely successful, has been show...
