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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 2, Pages 94–98 (Mi faa3269)  

Brief communications

Elements of Potential Theory on Carnot Groups

M. V. Ruzhanskya, D. Suraganba

a Imperial College, London, United Kingdom
b Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan

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.

Keywords: sub-Laplacian, integral boundary condition, homogeneous Carnot group, Newton potential, layer potentials.

Funding Agency Grant Number
Engineering and Physical Sciences Research Council EP/K039407/1
Leverhulme Trust RPG-2014-02
Ministry of Education and Science of the Republic of Kazakhstan AP05130981
The authors were supported in part by EPSRC grant EP/K039407/1, by Leverhulme Grant RPG-2014-02, and by MESRK grant AP05130981.


DOI: https://doi.org/10.4213/faa3269

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English version:
Functional Analysis and Its Applications, 2018, 52:2, 158–161

Bibliographic databases:

Document Type: Article
UDC: 517
Received: 10.02.2017

Citation: M. V. Ruzhansky, D. Suragan, “Elements of Potential Theory on Carnot Groups”, Funktsional. Anal. i Prilozhen., 52:2 (2018), 94–98; Funct. Anal. Appl., 52:2 (2018), 158–161

Citation in format AMSBIB
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\by M.~V.~Ruzhansky, D.~Suragan
\paper Elements of Potential Theory on Carnot Groups
\jour Funktsional. Anal. i Prilozhen.
\yr 2018
\vol 52
\issue 2
\pages 94--98
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\crossref{https://doi.org/10.4213/faa3269}
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\jour Funct. Anal. Appl.
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\vol 52
\issue 2
\pages 158--161
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