Imbedding estimates and elliptic equations with discontinuous coefficients in unbounded domains

In this paper we deal with the multiplication operator u ∈ W^{k,p} (Ω) → gu ∈ L^q (Ω), with g belonging to a space of Morrey type. We apply our results in order to establish an a-priori bound for the solutions of the Dirichlet problem concerning elliptic equations with discontinuous coefficients

Observing soil moisture temporal variability under fluctuating climatic conditions

International audienceThe paper focuses on the observation of interannual and intra-annual climate variability impact on soil moisture temporal patterns and variation, for an experimental site located in Southern Italy and characterized by a typical Mediterranean climate. Analysed data consist of three years soil water content time series measured during the period 2004?2007, under intermediate (2004/2005), wet (2005/2006) and dry (2006/2007) climatological conditions. Results show that, for the case study, interannual precipitation fluctuation highly impact the annual soil moisture cycle, modifying the number and length of characteristic periods revealed by the cycle patterns. Annual rainfall variation also affects the weight of the wet and dry soil moisture conditions, making the distinction between preferred states more and more evident for increasing precipitation variability. Intra-annual precipitation fluctuation instead mainly impact soil moisture dynamic during the dry period of the year, shifting the position of the modes and the weight of the wet mode and nearly leading the dry mode to disappear for larger mean seasonal rainfall. Reported analyses would be a support and a premise for further modeling implications

Fossil group origins: VIII RXJ075243.6+455653 a transitionary fossil group

It is thought that fossil systems are relics of structure formation in the primitive Universe. They are galaxy aggregations that have assembled their mass at high redshift with few or no subsequent accretion. Observationally these systems are selected by large magnitude gaps between their 1st and 2nd ranked galaxies. Nevertheless, there is still debate over whether or not this observational criterium selects dynamically evolved ancient systems. We have studied the properties of the nearby fossil group RXJ075243.6+455653 in order to understand the mass assembly of this system. Deep spectroscopic observations allow us to construct the galaxy luminosity function (LF) of RXJ075243.6+455653 down to M*+ 6. The analysis of the faint-end of the LF in groups and clusters provides valuable information about the mass assembly of the system. In addition, we have analyzed the nearby large-scale structure around this group. We identified 26 group members within r200=0.9 Mpc. The LF of the group shows a flat faint-end slope ( -1.08 +/- 0.33). This low density of dwarf galaxies is confirmed by the low value of the dwarf-to-giant ratio (DGR = 0.99 +/- 0.49) for this system. Both the lack of dwarf galaxies and the low luminosity of the BGG suggests that RXJ075243.6+455653 still has to accrete mass from its nearby environment. This mass accretion will be achieved because it is the dominant structure of a rich environment formed by several groups of galaxies (15) within 7 Mpc from the group center and with +/- 1000$ km/s. RXJ075243.6+455653 is a group of galaxies that has not yet completed the process of its mass assembly. This new mass accretion will change the fossil state of the group. This group is an example of a galaxy aggregation selected by a large magnitude gap but still in the process of the accretion of its mass (Abridged).Comment: 9 pages, 9 figures, accepted in A&

The planetary nebula population in the halo of M87

We investigate the diffuse light in the outer regions of the nearby elliptical galaxy M87 in the Virgo cluster, using planetary nebulas (PNs) as tracers. The surveyed areas (0.43 squared degrees) cover M87 up to a radial distance of 150 kpc, in the ransition region between galaxy halo and intracluster light (ICL). All PNs are identified through the on-off band technique using automatic selection criteria based on the distribution of the detected sources in the colour-magnitude diagram and the properties of their point-spread function. We extract a catalogue of 688 objects down to m_5007=28.4, with an estimated residual contamination from foreground stars and background Lyalpha galaxies, which amounts to ~35% of the sample. This is one of the largest extragalactic PN samples in number of candidates, magnitude depth, and radial extent, which allows us to carry out an unprecedented photometric study of the PN population in the outer regions of M87. We find that the logarithmic density profile of the PN distribution is shallower than the surface brightness profile at large radii. This behaviour is consistent with the superposition of two components associated with the halo of M87 and with the ICL, which have different luminosity specific PN numbers, the ICL contributing three times more PNs per unit light. Because of the depth of this survey we are also able to study the shape of the PN luminosity function (PNLF) in the outer regions of M87. We find a slope for the PNLF that is steeper at fainter magnitudes than the standard analytical PNLF formula and adopt a generalised model that treats the slope as a free parameter. Comparing the PNLF of M87 and the M31 bulge, both normalised by the sampled luminosity, the M87 PNLF contains fewer bright PNs and has a steeper slope towards fainter magnitudes.Comment: 16 pages, 13 figures, 5 tables, accepted for publication in A&