Math. Model. Nat. Phenom.
Volume 13, Number 4, 2018
|Number of page(s)||14|
|Published online||14 September 2018|
On green functions for Dirichelet sub-Laplacians on a Quaternion Heisenberg group
Institute of Mathematics and Mathematical Modeling,
125 Pushkin str., 050010
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: email@example.com
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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