LAUSR

Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups

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0 Published in 2017 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2016.12.013

Abstract: Abstract We propose the analogues of boundary layer potentials for the sub-Laplacian on homogeneous Carnot groups/stratified Lie groups and prove continuity results for them. In particular, we show continuity of the single layer potential and… read more here.

Keywords: sub laplacian; carnot groups; layer potentials; homogeneous carnot ... See more keywords

Rank-one theorem and subgraphs of BV functions in Carnot groups

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1 Published in 2019 at "Journal of Functional Analysis"

DOI: 10.1016/j.jfa.2018.09.016

Abstract: We prove a rank-one theorem \`a la G. Alberti for the derivatives of vector-valued maps with bounded variation in a class of Carnot groups that includes Heisenberg groups $\mathbb H^n$ for $n\geq 2$. The main… read more here.

Keywords: rank one; one theorem; subgraphs functions; theorem subgraphs ... See more keywords

Optimal decay of p-Sobolev extremals on Carnot groups

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1 Published in 2019 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2018.10.027

Abstract: Abstract We determine the sharp asymptotic behavior at infinity of solutions to quasilinear critical problems involving the p-sublaplacian operator Δ p , G on a Carnot group G , 1 p Q . As a… read more here.

Keywords: sobolev extremals; optimal decay; decay sobolev; carnot groups ... See more keywords

Exceptional families of measures on Carnot groups

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1 Published in 2022 at "Analysis and Geometry in Metric Spaces"

DOI: 10.1515/agms-2022-0148

Abstract: Abstract We study the families of measures on Carnot groups that have vanishing p p -module, which we call M p {M}_{p} -exceptional families. We found necessary and sufficient Conditions for the family of intrinsic… read more here.

Keywords: measures carnot; geometry; families measures; exceptional families ... See more keywords

Fractional Laplacians, perimeters and heat semigroups in Carnot groups

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0 Published in 2017 at "Discrete and Continuous Dynamical Systems - Series S"

DOI: 10.3934/dcdss.2018026

Abstract: We define and study the fractional Laplacian and the fractional perimeter of a set in Carnot groups and we compare the perimeter with the asymptotic behaviour of the fractional heat semigroup. read more here.

Keywords: heat semigroups; carnot groups; perimeters heat; laplacians perimeters ... See more keywords