A Variational Analysis of the Thermal Equilibrium State of Charged Quantum Fluids

Frank Pacard

doi:10.1080/03605309508821118

A Variational Analysis of the Thermal Equilibrium State of Charged Quantum Fluids

Frank Pacard

TU Berlin

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

The thermal equilibrium state of a charged, isentropic quantum fluid in a bounded domain Ω is entirely described by the particle density n minimizing the total energy where ϕ = V[n_] + V^e solves Poisson’s equation - Δϕ = n - C subject to mixed Dirichlet-Neumann boundary conditions. It is shown that for given N > 0 (i. e. for prescribed total number of particles) this energy functional admits a unique minimizer in Furthermore it is proven that n ε C_loc¹(Ω) H L^∞(Ω) for all λ ε (0,1) and n > 0 in Ω.

langue originale	Anglais
Pages (de - à)	885-900
Nombre de pages	16
journal	Communications in Partial Differential Equations
Volume	20
Numéro de publication	5-6
Les DOIs	https://doi.org/10.1080/03605309508821118
état	Publié - 1 janv. 1995
Modification externe	Oui

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10.1080/03605309508821118

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abstract = "The thermal equilibrium state of a charged, isentropic quantum fluid in a bounded domain Ω is entirely described by the particle density n minimizing the total energy where ϕ = V[n] + Ve solves Poisson{\textquoteright}s equation - Δϕ = n - C subject to mixed Dirichlet-Neumann boundary conditions. It is shown that for given N > 0 (i. e. for prescribed total number of particles) this energy functional admits a unique minimizer in Furthermore it is proven that n ε Cloc1(Ω) H L∞(Ω) for all λ ε (0,1) and n > 0 in Ω.",

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A Variational Analysis of the Thermal Equilibrium State of Charged Quantum Fluids

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