Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

A new CO carbonaceous chondrite from Acfer, Algeria

Many small fragments, totally weighing 118 g were found in the Acfer area by an Italian dealer. Chondrules size and types (predominance of granular olivine type), occurrence of twinned clinoenstatite and absence of plagioclase suggested a classification as CO carbonaceous chondrite

A new CH carbonaceous chondrite from Acfer, Algeria

A single stone weighing 1456 g was found in November 2002 in the Acfer area, Algeria. Oxygen isotope, chondrules-matrix ratio as well as other petrographic features point to a classification as CH carbonaceous chondrite

A new CK carbonaceous chondrite from Hammada Al Hamra, Libya

A single stone weighing 198 g was found in 2001 in the Hammada al Hamra region of Libya. Petrographic features (mean chondrules dimensions, coarse grained matrix and presence of AOIs and CAIs) point to a classification as CK carbonaceous chondrite

Correlated modal mineralogy, aqueous alteration and oxygen isotope composition of CM Chondrites

In this study we move beyond defining alteration sequences in CM chondrites towards understanding the relationship between modal mineralogy, the extent of aqueous alteration and O-isotope compositions