Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces

We develop arguments on convexity and minimization of energy functionals on Orlicz-Sobolev spaces to investigate existence of solution to the equation \displaystyle -\mbox{div} (\phi(|\nabla u|) \nabla u) = f(x,u) + h \mbox{in} \Omega under Dirichlet boundary conditions, where $\Omega \subset {\bf R}^{N}$ is a bounded smooth domain, $\phi : (0,\infty)\longrightarrow (0,\infty)$ is a suitable continuous function and $f: \Omega \times {\bf R} \to {\bf R}$ satisfies the Carath\'eodory conditions, while $h$ is a measure.Comment: 14 page

Scalar perturbations and the possible self-destruction of the phantom menace

Some analysis of the supernovae type Ia observational data seems to indicate that the Universe today is dominated by a phantom field, for which all energy conditions are violated. Such phantom field may imply a singularity in a future finite time, called big rip. Studying the evolution of scalar perturbations for such a field, we show that if the pressure is negative enough, the Universe can become highly inhomogeneous and this phantom menace may be avoided.Comment: Latex file, 5 page

Vector Meson Production in Coherent Hadronic Interactions: An update on predictions for RHIC and LHC

In this letter we update our predictions for the photoproduction of vector mesons in coherent $pp$ and $AA$ collisions at RHIC and LHC energies using the color dipole approach and the Color Glass Condensate (CGC) formalism. In particular, we present our predictions for the first run of the LHC at half energy and for the rapidity dependence of the ratio between the $J/\Psi$ and $\rho$ cross sections at RHIC energies.Comment: 4 pages, 3 figure