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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

Dirichlet Sub-Laplacians on Homogeneous Carnot Groups: Spectral Properties, Asymptotics, and Heat Content

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1 Published in 2022 at "International Mathematics Research Notices"

DOI: 10.1093/imrn/rnad065

Abstract: We consider sub-Laplacians in open bounded sets in a homogeneous Carnot group and study their spectral properties. We prove that these operators have a pure point spectrum and prove the existence of the spectral gap.… read more here.

Keywords: sub laplacians; homogeneous carnot; dirichlet sub; heat content ... See more keywords