On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications

We prove the Lewy-Stampacchia inequalities for the two obstacles problem in abstract form for T-monotone operators. As a consequence for a general class of quasi-linear elliptic operators of Ladyzhenskaya-Uraltseva type, including p(x)-Laplacian type operators, we derive new results of $C^{1,\alpha}$ regularity for the solution. We also apply those inequalities to obtain new results to the N-membranes problem and the regularity and monotonicity properties to obtain the existence of a solution to a quasi-variational problem in (generalized) Orlicz-Sobolev spaces

A method for evaluating models that use galaxy rotation curves to derive the density profiles

There are some approaches, either based on General Relativity (GR) or modified gravity, that use galaxy rotation curves to derive the matter density of the corresponding galaxy, and this procedure would either indicate a partial or a complete elimination of dark matter in galaxies. Here we review these approaches, clarify the difficulties on this inverted procedure, present a method for evaluating them, and use it to test two specific approaches that are based on GR: the Cooperstock-Tieu (CT) and the Balasin-Grumiller (BG) approaches. Using this new method, we find that neither of the tested approaches can satisfactorily fit the observational data without dark matter. The CT approach results can be significantly improved if some dark matter is considered, while for the BG approach no usual dark matter halo can improve its results.Comment: 11 pages, 2 figures, 4 tables. v2: diverse text improvements, no changes in the conclusions. Version accepted in MNRA

The runaway black hole GRO J1655-40

We have used the Hubble Space Telescope to measure the motion in the sky and compute the galactocentric orbit of the black hole X-ray binary GRO J1655-40. The system moves with a runaway space velocity of $112\pm 18$ km s$^{-1}$ in a highly eccentric ($e = 0.34\pm 0.05$) orbit. The black hole was formed in the disk at a distance greater than 3 kpc from the Galactic centre and must have been shot to such an eccentric orbit by the explosion of the progenitor star. The runaway linear momentum and kinetic energy of this black hole binary are comparable to those of solitary neutron stars and millisecond pulsars. GRO J1655-40 is the first black hole for which there is evidence for a runaway motion imparted by a natal kick in a supernova explosion.Comment: Published in Astronomy and Astrophysics. 5 pages, 2 color figures. Color figure and animation can be found at http://www.iafe.uba.ar/astronomia/mirabel/mirabel.html or ftp://ftp.cea.fr/incoming/y2k01/mirabe