Uniqueness and radial symmetry of minimizers for a nonlocal variational problem

Orlando Lopes

Uniqueness and radial symmetry of minimizers for a nonlocal variational problem

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arxiv 1706.04070 v1 pith:HJ5VCY7O submitted 2017-06-13 math.AP

Orlando Lopes This is my paper · ORCID

classification math.AP

keywords uniquenessminimizersradialsymmetryvariationalconsequenceconvexitydistributions

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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.

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Uniqueness and non-uniqueness of steady states of aggregation-diffusion equations
math.AP 2019-08 accept novelty 8.0 of 10

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.

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