@article{pacard_variational_1995,
title = {A {Variational} {Analysis} {Of} {The} {Thermal}-{Equilibrium} {State} {Of} {Charged} {Quantum} {Fluids}},
volume = {20},
abstract = {The thermal equilibrium state of a charged, isentropic quantum fluid in a bounded domain Omega is entirely described by the particle density n minimizing the total energy E(n) = integral(Omega){\textbackslash}backslashdel root n{\textbackslash}backslash(2) + integral(Omega)H(n) + 1/2 integral(Omega)nV[n] + integral(Omega)V(e)n where Phi = V[n] + V-e solves Poisson’s equation -Delta Phi = n – C subject to mixed Dirichlet-Neumann boundary conditions. It is shown that for given N {\textgreater} 0 (i. e. for prescribed total number of particles) this energy functional admits a unique minimizer in \{n is an element of L(1) (Omega); n greater than or equal to 0, integral(Omega) n = N, root n is an element of H-1 (Omega)\} Furthermore it is proven that n is an element of C-loc(1,lambda)(Omega)boolean AND L(infinity)(Omega) for all lambda is an element of (0, 1) and n {\textgreater} 0 in Omega.},
number = {5-6},
journal = {Communications in Partial Differential Equations},
author = {Pacard, F. and Unterreiter, A.},
year = {1995},
pages = {885--900},
}