TY - JOUR
T1 - On green functions for Dirichelet sub-Laplacians on a Quaternion Heisenberg group
AU - Sabitbek, Bolys
AU - Suragan, Durvudkhan
N1 - Publisher Copyright:
© EDP Sciences, 2018.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Dirichlet sub-Laplacian
KW - Green function
KW - Quaternion Heisenberg group
UR - http://www.scopus.com/inward/record.url?scp=85053629763&partnerID=8YFLogxK
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U2 - 10.1051/mmnp/2018042
DO - 10.1051/mmnp/2018042
M3 - Article
AN - SCOPUS:85053629763
SN - 0973-5348
VL - 13
JO - Mathematical Modelling of Natural Phenomena
JF - Mathematical Modelling of Natural Phenomena
IS - 4
M1 - 39
ER -