| Issue |
Math. Model. Nat. Phenom.
Volume 13, Number 4, 2018
Harmonic analysis
|
|
|---|---|---|
| Article Number | 39 | |
| Number of page(s) | 14 | |
| DOI | https://doi.org/10.1051/mmnp/2018042 | |
| Published online | 14 September 2018 | |
On green functions for Dirichelet sub-Laplacians on a Quaternion Heisenberg group
1
Institute of Mathematics and Mathematical Modeling,
125 Pushkin str., 050010
Almaty, Kazakhstan
2
al-Farabi Kazakh National University,
71 al-Farabi ave., 050040
Almaty, Kazakhstan
3
Department of Mathematics,
School of Science and Technology, Nazarbayev University,
53 Kabanbay Batyr Ave,
Astana 010000, Kazakhstan
* Corresponding author: b.sabitbek@math.kz
Accepted: 15 March 2018
In the present paper, Green functions of Dirichlet boundary value problems are constructed for sub-Laplacians on certain unbounded domains of the quaternion Heisenberg group. Also, the explicit solutions of the Dirichlet problem are presented for the sub-Laplacian with non-zero boundary datum in wedge and strip domains. We also present Hardy and Rellich inequalities for the sub-Laplacians in terms of their fundamental solutions.
Mathematics Subject Classification: 22E30 / 43A80
Key words: Green function / Dirichlet sub-Laplacian / quaternion Heisenberg group
© EDP Sciences, 2018
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