Functional Analysis and Its Applications

, Volume 52, Issue 2, pp 158–161 | Cite as

Elements of Potential Theory on Carnot Groups

  • M. V. Ruzhansky
  • D. Suragan


We propose and study elements of potential theory for the sub-Laplacian on homogeneous Carnot groups. In particular, we show the continuity of the single-layer potential and establish Plemelj-type jump relations for the double-layer potential. As a consequence, we derive a formula for the trace on smooth surfaces of the Newton potential for the sub-Laplacian. Using this, we construct a sub-Laplacian version of Kac’s boundary value problem.

Key words

sub-Laplacian integral boundary condition homogeneous Carnot group Newton potential layer potentials 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Imperial CollegeLondonUnited Kingdom
  2. 2.Institute of Mathematics and Mathematical ModellingAlmatyKazakhstan

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