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’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.
| Original language | English |
|---|---|
| Pages (from-to) | 885-900 |
| Number of pages | 16 |
| Journal | Communications in Partial Differential Equations |
| Volume | 20 |
| Issue number | 5-6 |
| DOIs | |
| Publication status | Published - 1 Jan 1995 |
| Externally published | Yes |
Keywords
- thermal equilibrium state of quantum fluid quantum hydrodynamic model variational method for a semilinear elliptic system boundary value problem for nonlinear elliptic PDE a priori estimates smoothness and positivity of energy minimizer variational principles in thermodynamics
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