For aggregation-diffusion equations with attractive potentials, this paper proves steady states of fixed mass are unique iff m >= 2, and constructs non-uniqueness examples for 1 < m < 2.
Uniqueness and radial symmetry of minimizers for a nonlocal variational problem
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper we prove the uniqueness and radial symmetry of minimizers for variational problems that model several phenomena. The uniqueness is a consequence of the convexity of the functional. The main technique is Fourier transform of tempered distributions.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2019 1verdicts
ACCEPT 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Uniqueness and non-uniqueness of steady states of aggregation-diffusion equations
For aggregation-diffusion equations with attractive potentials, this paper proves steady states of fixed mass are unique iff m >= 2, and constructs non-uniqueness examples for 1 < m < 2.