This open access book provides an extensive treatment of Hardy inequalities and closely
related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The …

Given a large ensemble of interacting particles, driven by nonlocal interactions and localized
repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential …

We develop a weak-form sparse identification method for interacting particle systems (IPS)
with the primary goals of reducing computational complexity for large particle number N and …

The aim of this survey is to serve as an introduction to the different techniques available in
the broad field of aggregation-diffusion equations. We aim to provide historical context, key …

For the interaction energy with repulsive–attractive potentials, we give generic conditions
which guarantee the radial symmetry of the local minimizers in the infinite Wasserstein …

We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-
linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known …

We consider a nonlocal aggregation equation with degenerate diffusion, which describes
the mean‐field limit of interacting particles driven by nonlocal interactions and localized …

This paper is devoted to a new family of reverse Hardy–Littlewood–Sobolev inequalities
which involve a power law kernel with positive exponent. We investigate the range of the …

In this paper we characterise the minimisers of a one-parameter family of nonlocal and
anisotropic energies I α defined on probability measures in R n, with n≥ 3. The energy I α …

We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion
equations with linear diffusion. As soon as the interaction potential is bounded and its first …