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.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05
English
entropy maximization
non local elliptic equations with exponential nonlinearity
D. Bartolucci is partially supported by MIUR Excellence Department Project awarded to the Department of Mathematics, Univ. of Rome Tor Vergata, CUP E83C18000100006. G. Wolansky is partially supported by ISF grant 988/15
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].
Bartolucci, D; Wolansky, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/256327
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