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

Sub-Laplacian
Carnot Group
Potential Theory
Boundary value problems
Double Layer Potential
Single Layer Potential
Homogeneous Groups
Smooth surface
Jump
Boundary Value Problem
Trace

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Elements of Potential Theory on Carnot Groups. / Ruzhansky, M. V.; Suragan, D.

In: Functional Analysis and its Applications, Vol. 52, No. 2, 01.04.2018, p. 158-161.

Research output: Contribution to journalArticle

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