Elements of Potential Theory on Carnot Groups

M. V. Ruzhansky, D. Suragan

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)158-161
Number of pages4
JournalFunctional Analysis and its Applications
Issue number2
Publication statusPublished - Apr 1 2018
Externally publishedYes


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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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