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Our recent work on the Burchard-Choksi-Topaloglu flocking problem showed that in the large mass regime the ground state density profile is the characteristic function of some set.
C. A. Rogers, A single integral inequality
1909
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F. Riesz, Sur une inégalité intégrale
1930
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H. J. Brascamp, E. H. Lieb, J. M. Luttinger, A general rearrangement inequality for multiple integrals
1974
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H. Brezis, E. H. Lieb, Sobolev inequalities with remainder terms
1985
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F. J. Almgren Jr., E. H. Lieb, Symmetric decreasing rearrangement is sometimes continuous
1989
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G. Bianchi, H. Egnell, A note on the Sobolev inequality
1991
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H. Knüpfer, C. B. Muratov, On an isoperimetric problem with a competing nonlocal term II: The general case
1994
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E. H. Lieb, M. Loss, Analysis
2001
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R. L. Frank, R. Seiringer, Non-linear ground state representations and sharp Hardy inequalities
2008
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S. Chen, R. L. Frank, T. Weth, Remainder terms in the fractional Sobolev inequality
2013
Cited alongside, same era.
H. Knüpfer, C. B. Muratov, On an isoperimetric problem with a competing nonlocal term I: The planar case
2013
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M. Bonacini, R. Cristoferi, Local and global minimality results for a nonlocal isoperimetric problem on ℝ N \mathbb{R}^{N}
2014
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V. Julin, Isoperimetric problem with a Coulomb repulsive term
2014
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A. Burchard, G. R. Chambers, Geometric stability of the Coulomb energy
2015
Cited alongside, same era.
R. Choksi, R. C. Fetecau, I. Topaloglu, On minimizers of interaction functionals with competing attractive and repulsive potentials
R. Choksi, C. B. Muratov, I. Topaloglu, An old problem resurfaces nonlocally: Gamow’s liquid drops inspire today’s research and applications
2017
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M. Christ, A sharpened Riesz–Sobolev inequality
2017
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M. Christ, Equality in Brascamp–Lieb–Luttinger inequalities
2017
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M. Christ, K. O’Neill, Maximizers of Rogers–Brascamp–Lieb–Luttinger functionals in higher dimensions
2017
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A. Burchard, R. Choksi, I. Topaloglu, Nonlocal shape optimization via interactions of attractive and repulsive potentials
2018
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2015
Cited alongside, same era.
A. Figalli, N. Fusco, F. Maggi, V. Millot, M. Morini, Isoperimetry and stability properties of balls with respect to nonlocal energies
2015
Cited alongside, same era.
R. L. Frank, E. H. Lieb, A compactness lemma and its application to the existence of minimizers for the liquid drop model
2015
Cited alongside, same era.
R. L. Frank, E. H. Lieb, A note on a theorem of M. Christ
Cited in the paper.
M. Christ, M. Iliopoulou, Inequalities of Riesz–Sobolev type for compact connected Abelian groups
2018
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R. L. Frank, E. H. Lieb, A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions
2018
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O. Lopes, Uniqueness and radial symmetry of minimizers for a nonlocal variational problem
2019
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