Special Session 77: Singularity and regularity in nonlinear PDEs

Competing effects in fractional thin film equations
Antonio Esposito
University of L'Aquila
Italy
Co-Author(s):    
Abstract:
The talk concerns the analysis of fractional thin film equations with linear mobility and an aggregation term. The problem is posed in a bounded convex domain with homogeneous Neumann boundary conditions, in dimension $d \geq 1$. We study the existence of weak solutions by interpreting the problem as a 2-Wasserstein gradient flow of an energy functional presenting two competing effects: the fractional Dirichlet energy and the power-law internal energy. The seminar is based on a joint work with J. A. Carrillo, A. Massucco, and S. Lisini.