Partial regularity for manifold constrained p(x)-harmonic maps

We prove that manifold constrained $p(x)$-harmonic maps are $C^{1,\beta}$-regular outside a set of zero $n$-dimensional Lebesgue's measure, for some $\beta \in (0,1)$. We also provide an estimate from above of the Hausdorff dimension of the singular set

Higher Integrability for Constrained Minimizers of Integral Functionals with (p,q)-Growth in low dimension

We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations with (p,q)-Growth conditions in low dimension. Our procedure is set in the framework of Fractional Sobolev Spaces and renders the desired regularity as the result of an approximation technique relying on estimates obtained through a careful use of difference quotients.Comment: 22 pages, 0 figure

Abell 370: A Cluster with a Pronounced Triaxial Morphology

We here combine Sunyaev-Zel'dovich effect, X-ray observations and spectroscopic redshifts of member galaxies, to constrain the intrinsic three-dimensional shape of the galaxy cluster: Abell 370. The cluster turns out to be strongly elongated along the l.o.s., with two (or more) substructures in the process of merging. Spectroscopy further suggests that the process must be taking place at a small angle respect to the l.o.s.Comment: 7 pages, 2 figures. Contribution to the Proceedings of the COSPAR Scientific Assembly, E1.2 "Clusters of Galaxies: New Insights from XMM-Newton, Chandra and INTEGRAL", Paris (France), July 19-20, 2004. Accepted for publication in Advances in Space Researc

Manifold constrained non-uniformly elliptic problems

We consider the problem of minimizing variational integrals defined on \cc{nonlinear} Sobolev spaces of competitors taking values into the sphere. The main novelty is that the underlying energy features a non-uniformly elliptic integrand exhibiting different polynomial growth conditions and no homogeneity. We develop a few intrinsic methods aimed at proving partial regularity of minima and providing techniques for treating larger classes of similar constrained non-uniformly elliptic variational problems. In order to give estimates for the singular sets we use a general family of Hausdorff type measures following the local geometry of the integrand. A suitable comparison is provided with respect to the naturally associated capacities.Comment: 50 page

On the regularity of minima of non-autonomous functionals

We consider regularity issues for minima of non-autonomous functionals in the Calculus of Variations exhibiting non-uniform ellipticity features. We provide a few sharp regularity results for local minimizers that also cover the case of functionals with nearly linear growth. The analysis is carried out provided certain necessary approximation-in-energy conditions are satisfied. These are related to the occurrence of the so-called Lavrentiev phenomenon that that non-autonomous functionals might exhibit, and which is a natural obstruction to regularity. In the case of vector valued problems we concentrate on higher gradient integrability of minima. Instead, in the scalar case, we prove local Lipschitz estimates. We also present an approach via a variant of Moser's iteration technique that allows to reduce the analysis of several non-uniformly elliptic problems to that for uniformly elliptic ones.Comment: 32 page

Normal state properties of an interacting large polaron gas

A simple approach to the many-polaron problem for both weak and intermediate electron-phonon coupling and valid for densities much smaller than those typical of metals is presented. Within the model the total energy, the collective modes and the single-particle properties are studied and compared with the available theories. It is shown the occurrence of a charge density wave instability in the intermediate coupling regime.Comment: 26 pages, 12 figures. To appear on European Physical Journal

Modelling clusters of galaxies by f(R)-gravity

We consider the possibility that masses and gravitational potentials of galaxy cluster, estimated at X-ray wavelengths, could be explained without assuming huge amounts of dark matter, but in the context of $f(R)$-gravity. Specifically, we take into account the weak field limit of such theories and show that the corrected gravitational potential allows to estimate the total mass of a sample of 12 clusters of galaxies. Results show that such a gravitational potential provides a fair fit to the mass of visible matter (i.e. gas + stars) estimated by X-ray observations, without the need of additional dark matter while the size of the clusters, as already observed at different scale for galaxies, strictly depends on the interaction lengths of the corrections to the Newtonian potential.Comment: 18 pages, 34 figure

An Innovative Mission Management System for Fixed-Wing UAVs

This paper presents two innovative units linked together to build the main frame of a UAV Mis- sion Management System. The first unit is a Path Planner for small UAVs able to generate optimal paths in a tridimensional environment, generat- ing flyable and safe paths with the lowest com- putational effort. The second unit is the Flight Management System based on Nonlinear Model Predictive Control, that tracks the reference path and exploits a spherical camera model to avoid unpredicted obstacles along the path. The control system solves on-line (i.e. at each sampling time) a finite horizon (state horizon) open loop optimal control problem with a Genetic Algorithm. This algorithm finds the command sequence that min- imizes the tracking error with respect to the ref- erence path, driving the aircraft far from sensed obstacles and towards the desired trajectory

Optical properties of an interacting large polaron gas

The normal state conductivity of a system of interacting large polarons is calculated within the Random Phase approximation and some numerical results are presented. The behaviour of the optical absorption as a function of the charge carrier density and of the temperature is analyzed for different values of the electron-phonon coupling constant. It is shown that the conductivity exihibits features similar to thos observed in the infrared spectra of the cuprates.Comment: 13 pages, 1 table, 3 figures (to be published ob Eur. Jour. Phys. B