Elements of Potential Theory on Carnot Groups

M. V. Ruzhansky, D. Suragan

Research output: Contribution to journalArticle

Abstract

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
Volume52
Issue number2
DOIs
Publication statusPublished - Apr 1 2018
Externally publishedYes

    Fingerprint

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this