Fetching the paper…
Reading the bibliography…
We show that the support of any local minimizer of the interaction energy consists of isolated points whenever the interaction potential is of class $C^2$ and mildly repulsive at the origin; moreover, if the minimizer is global, then its support is finite.
A non-local model for a swarm
A. Mogilner and L. Edelstein-Keshet · 1999
Earlier work this paper cites.
One-dimensional kinetic models of granular flows
G. Toscani · 2000
Earlier work this paper cites.
Topics in Optimal Transportation
C. Villani · 2003
Earlier work this paper cites.
Self-propelled particles with soft-core interactions: patterns, stability, and collapse
M. R. D’Orsogna, Y.-L. Chuang, A. L. Bertozzi, and L. S. Chayes · 2006
Earlier work this paper cites.
Formation of clumps and patches in self-aggregation of finite-size particles
D. D. Holm and V. Putkaradze · 2006
Earlier work this paper cites.
A nonlocal continuum model for biological aggregation
C. M. Topaz, A. L. Bertozzi, and M. A. Lewis · 2006
Earlier work this paper cites.
Stability of ring patterns arising from two-dimensional particle interactions
T. Kolokolnikov, H. Sun, D. Uminsky, and A. L. Bertozzi · 2011
Cited alongside, same era.
Dimensionality of local minimizers of the interaction energy
D. Balagué, J. A. Carrillo, T. Laurent, and G. Raoul · 2013
Cited alongside, same era.
Relative entropy in diffusive relaxation
C. Lattanzio and A. E. Tzavaras · 2013
Cited alongside, same era.
Stability analysis of flock and mill rings for second order models in swarming
G. Albi, D. Balagué, J. A. Carrillo, and J. Von Brecht · 2014
Cited alongside, same era.
From Nash to Cournot–Nash equilibria via the Monge–Kantorovich problem
A. Blanchet and G. Carlier · 2014
Cited alongside, same era.
Ring patterns and their bifurcations in a nonlocal model of biological swarms
A. L. Bertozzi, T. Kolokolnikov, H. Sun, D. Uminsky, and J. Von Brecht · 2015
Existence of compactly supported global minimisers for the interaction energy
J. A. Cañizo, J. A. Carrillo, and F. S. Patacchini · 2015
Later among the works it cites.
Ground states for diffusion dominated free energies with logarithmic interaction
J. A. Carrillo, D. Castorina, and B. Volzone · 2015
Later among the works it cites.
Some free boundary problems involving non-local diffusion and aggregation
J. A. Carrillo and J. L. Vázquez · 2015
Later among the works it cites.
Existence of ground states of nonlocal-interaction energies
R. Simione, D. Slepčev, and I. Topaloglu · 2015
Later among the works it cites.
Regularity of local minimizers of the interaction energy via obstacle problems
J. A. Carrillo, M. G. Delgadino, and A. Mellet · 2016
Closest in time.
Explicit equilibrium solutions for the aggregation equation with power-law potentials
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
J. A. Carrillo and Y. Huang · 2016
Closest in time.