New oxygen isotope evidence for the origin of mesosiderites and main group pallasites

High precision oxygen isotope analyses reveal that the silicate portion of mesosiderites are indistinguishable from the HEDs and suggest a common origin. However, the main group pallasites have a distinct signature, and therefore different source

Hydrogen isotopic composition of the Tagish Lake meteorite: comparison with other carbonaceous chondrites

A study into the hydrogen isotopic characteristics of whole rock samples of carbonaceous chondrites and their comparison with a whole rock sample of the Tagish Lake meteorite

How Useful are High-Precision Delta ?17O Data in Defining the Asteroidal Sources of Meteorites?: Evidence from Main-Group Pallasites, Primitive and Differentiated Achondrites

High-precision oxygen isotope analysis is capable of revealing important information about the relationship between different meteorite groups. New data confirm that the main-group pallasites are from a distinct source to either the HEDs or mesosiderites

Harnack inequality for fractional sub-Laplacians in Carnot groups

In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre. In addition, we write explicitly the Poisson kernel for a class of degenerate subelliptic equations in product-type Carnot groups

Approximations of Sobolev norms in Carnot groups

This paper deals with a notion of Sobolev space $W^{1,p}$ introduced by J.Bourgain, H.Brezis and P.Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by A.Ponce to obtain a Poincar\'e-type inequality. The main results that we present are a generalization of these two works to a non-Euclidean setting, namely that of Carnot groups. We show that the seminorm expressd in terms of the intrinsic distance is equivalent to the $L^p$ norm of the intrinsic gradient, and provide a Poincar\'e-type inequality on Carnot groups by means of a constructive approach which relies on one-dimensional estimates. Self-improving properties are also studied for some cases of interest