3,703 research outputs found
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
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Organic components in interplanetary dust particles and their implications for the synthesis of cometary organics
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
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Asteroidal differentiation processes deduced from ultramafic achondrite ureilite meteorites
Ureilite meteorites are partial melt residues of an asteroid-sized object. They record the differentiation process that transformed many asteroids during the earliest stages of solar system formation
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
weight. Regularity results are achieved under minimal assumptions on the
coefficients and, as an application, we prove local estimates
for solutions of a degenerate equation in non divergence form
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Solar and solar-wind oxygen isotopes and the Genesis mission
The solar oxygen isotope composition is thought to hold important clues to pre-planetary processing of materials in the solar nebula, yet it is essentially unmeasured. Here we describe plans for O isotope analyses of Genesis solar-wind samples
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Insight into the evolution of the Tagish Lake carbonaceous chondrite by analysis of the oxygen isotopic composition of extracted water and Mössbauer spectroscopy
Analysis of oxygen isotopes in water from Tagish Lake together with Mössbauer Spectroscopy suggest some similarities to the CI group of meteorites but also suggest differences in the extent of parent body hydrothermal alteration
Multiple pulses of aqueous solutions in QUE 93005 (CM2): evidence from oxygen isotopes
No abstract available
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Amino acids composition and oxygen isotopes in the Shisr 033 CR chondrite
Approximations of Sobolev norms in Carnot groups
This paper deals with a notion of Sobolev space 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 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
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