Nonlinear Diffusion and related PDEs in (non) Euclidean Settings

The analysis of nonlinear diffusion PDEs is a wide field of research that not only encompasses elliptic and parabolic equations, but also includes several functional-analytic tools that proved successful in the deep understanding of such equations: just to mention a few, we recall Hardy, Poincaré and Sobolev inequalities. The corresponding rigorous theory, at least in the Euclidean setting, has reached extremely high levels, both in the local and the nonlocal case, with many sharp results available by now. The general interest for such equations is motivated by the fact that they are of paramount importance in the description and modeling of a number of real-world phenomena (e.g., the flow of gases through a porous medium, water infiltration, heat dispersion, population dynamics, etc...).