Maximal entropy solutions under prescribed mass and energy

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Bartolucci, Daniele¹  Wolansky, Gershon² 

[1] Univ Roma Tor Vergata, Dept Math, Via Ric Sci 1, I-00133 Rome, Italy

[2] Technion, Dept Math, IL-32000 Haifa, Israel

关键词: Entropy maximization;    Non local elliptic equations with exponential nonlinearity;   

DOI  :  10.1016/j.jde.2019.11.040

来源: Elsevier

【 摘 要 】

We consider a non-local elliptic equation with exponential nonlinearity, closely related to the mean field Liouville equation. The motivation for this equation is a variational entropy maximization problem under prescribed mass and energy. We provide an unconditional existence proof in case of electrostatic (repulsive) self-interaction, and conditional existence and uniqueness in dimension two in the case of gravitational (attractive) self-interaction. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free