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.
Bartolucci, D., Wolansky, G. (2020). Maximal entropy solutions under prescribed mass and energy. JOURNAL OF DIFFERENTIAL EQUATIONS, 268(11), 6646-6665 [10.1016/j.jde.2019.11.040].
Maximal entropy solutions under prescribed mass and energy
Bartolucci, D
Membro del Collaboration Group
;
2020-01-01
Abstract
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.| File | Dimensione | Formato | |
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