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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.
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
Linking options:
https://www.mathnet.ru/eng/faa3269https://doi.org/10.4213/faa3269 https://www.mathnet.ru/eng/faa/v52/i2/p94
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