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1
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How to get rid of one of the weights in a two-weight Poincaré inequality?

100%
Franchi B., Hajłasz P.
Annales Polonici Mathematici
|
2000
|
tom 74
|
nr 1
97-103
EN
We prove that if a Poincaré inequality with two different weights holds on every ball, then a Poincaré inequality with the same weight on both sides holds as well.
2
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Compensation couples and isoperimetric estimates for vector fields

100%
Franchi B., Wheeden R. L.
Colloquium Mathematicum
|
1997
|
tom 74
|
nr 1
9-27
3
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Gehring's lemma for metrics and higher integrability of the gradient for minimizers of noncoercive variational functionals

100%
Franchi B., Cassano F. S.
Studia Mathematica
|
1996
|
tom 120
|
nr 1
1-22
EN
We prove a higher integrability result - similar to Gehring's lemma - for the metric space associated with a family of Lipschitz continuous vector fields by means of sub-unit curves. Applications are given to show the higher integrability of the gradient of minimizers of some noncoercive variational functionals.
4
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Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem

81%
Franchi B., Marchi M., Serapioni R. P.
Analysis and Geometry in Metric Spaces
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2014
|
tom 2
|
nr 1
EN
A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups. Both seem to be the natural analogues inside Carnot groups of the corresponding Euclidean notions. Here ‘natural’ is meant to stress that the intrinsic notions depend only on the structure of the algebra of G. We prove that one codimensional intrinsic Lipschitz graphs are sets with locally finite G-perimeter. From this a Rademacher’s type theorem for one codimensional graphs in a general class of groups is proved.
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