Elements of Potential Theory on Carnot Groups
File(s)RS_FAA_short-1.pdf (232.29 KB)
Accepted version
Author(s)
Ruzhansky, MV
Suragan, D
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.
Date Issued
2018-07-07
Date Acceptance
2018-07-01
Citation
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2018, 52 (2), pp.158-161
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
Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000437825500011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/K039407/1
RPG-2014-002
Subjects
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
Publication Status
Published
Date Publish Online
2018-07-07