A "liquid-solid" phase transition in a simple model for swarming, based on the "no flat-spots" theorem for subharmonic functions
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Publication:4962409
DOI10.1512/iumj.2018.67.7398zbMath1420.49040arXiv1607.07971OpenAlexW2620806331WikidataQ129322695 ScholiaQ129322695MaRDI QIDQ4962409
Elliott H. Lieb, Rupert L. Frank
Publication date: 2 November 2018
Published in: Indiana University Mathematics Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1607.07971
Regularity of solutions in optimal control (49N60) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Optimization of shapes other than minimal surfaces (49Q10)
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- Absolute continuity on tracks and mappings of Sobolev spaces
- Partial regularity of solutions of fully nonlinear, uniformly elliptic equations
- Nonexistence of a Minimizer for Thomas-Fermi-Dirac-von Weizsäcker Model
- A Primer of Swarm Equilibria
- Swarm dynamics and equilibria for a nonlocal aggregation model
- Symmetric Decreasing Rearrangement Is Sometimes Continuous
- Hahn decomposition for the Riesz charge of $\delta$-subharmonic functions
- Nonlocal Shape Optimization via Interactions of Attractive and Repulsive Potentials
- A General Chain Rule for Derivatives and the Change of Variables Formula for the Lebesgue Integral
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