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

White dwarfs with a surface electrical charge distribution: Equilibrium and stability

The equilibrium configuration and the radial stability of white dwarfs composed of charged perfect fluid are investigated. These cases are analyzed through the results obtained from the solution of the hydrostatic equilibrium equation. We regard that the fluid pressure and the fluid energy density follow the relation of a fully degenerate electron gas. For the electric charge distribution in the object, we consider that it is centralized only close to the white dwarfs' surfaces. We obtain larger and more massive white dwarfs when the total electric charge is increased. To appreciate the effects of the electric charge in the structure of the star, we found that it must be in the order of $10^{20}\,[{\rm C}]$ with which the electric field is about $10^{16}\,[{\rm V/cm}]$. For white dwarfs with electric fields close to the Schwinger limit, we obtain masses around $2\,M_{\odot}$. We also found that in a system constituted by charged static equilibrium configurations, the maximum mass point found on it marks the onset of the instability. This indicates that the necessary and sufficient conditions to recognize regions constituted by stable and unstable equilibrium configurations against small radial perturbations are respectively $dM/d\rho_c>0$ and $dM/d\rho_c<0$.Comment: This is a preprint. The original paper will be published in EPJ