Elements of Potential Theory on Carnot Groups

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Title: Elements of Potential Theory on Carnot Groups
Authors: Ruzhansky, MV
Suragan, D
Item Type: Journal Article
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.
Issue Date: 7-Jul-2018
Date of Acceptance: 1-Jul-2018
URI: http://hdl.handle.net/10044/1/62251
DOI: https://dx.doi.org/10.1007/s10688-018-0224-5
ISSN: 0016-2663
Publisher: PLEIADES PUBLISHING INC
Start Page: 158
End Page: 161
Journal / Book Title: FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
Volume: 52
Issue: 2
Copyright Statement: © 2018 Springer Science+Business Media, LLC, part of Springer Nature. The final publication is available at https://dx.doi.org/10.1007/s10688-018-0224-5
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
RPG-2014-002
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
sub-Laplacian
integral boundary condition
homogeneous Carnot group
Newton potential
layer potentials
HEISENBERG-GROUP
DIRICHLET PROBLEM
KOHN-LAPLACIAN
CALCULUS
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Publication Status: Published
Online Publication Date: 2018-07-07
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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