Regularity of Local Minimizers of the Interaction Energy Via Obstacle Problems
File(s)
Published version
Author(s)
Carrillo de la Plata, J
Delgadino, MG
Mellet, A
Type
Journal Article
Abstract
The repulsion strength at the origin for repulsive/attractive potentials determines
the regularity of local minimizers of the interaction energy. In this paper, we
show that if this repulsion is like Newtonian or more singular than Newtonian (but still
locally integrable), then the local minimizers must be locally bounded densities (and
even continuous for more singular than Newtonian repulsion). We prove this (and some
other regularity results) by first showing that the potential function associated to a local
minimizer solves an obstacle problem and then by using classical regularity results for
such problems.
the regularity of local minimizers of the interaction energy. In this paper, we
show that if this repulsion is like Newtonian or more singular than Newtonian (but still
locally integrable), then the local minimizers must be locally bounded densities (and
even continuous for more singular than Newtonian repulsion). We prove this (and some
other regularity results) by first showing that the potential function associated to a local
minimizer solves an obstacle problem and then by using classical regularity results for
such problems.
Date Issued
2016-05-01
Date Acceptance
2016-01-23
Citation
Communications in Mathematical Physics, 2016, 343 (3), pp.747-781
ISSN
1432-0916
Publisher
Springer Verlag (Germany)
Start Page
747
End Page
781
Journal / Book Title
Communications in Mathematical Physics
Volume
343
Issue
3
Copyright Statement
© The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
License URL
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM120001
EP/K008404/1
Subjects
Science & Technology
Physical Sciences
Physics, Mathematical
Physics
STATIONARY STATES
NONLOCAL EQUATIONS
FREE-BOUNDARY
STABILITY
AGGREGATION
ASYMPTOTICS
POTENTIALS
BEHAVIOR
MODELS
FLOCK
math.AP
math.AP
Mathematical Physics
0101 Pure Mathematics
0105 Mathematical Physics
0206 Quantum Physics
Publication Status
Published
Date Publish Online
2016-03-17