On green functions for Dirichelet sub-Laplacians on a Quaternion Heisenberg group

Bolys Sabitbek; Durvudkhan Suragan

doi:10.1051/mmnp/2018042

On green functions for Dirichelet sub-Laplacians on a Quaternion Heisenberg group

Bolys Sabitbek
, Durvudkhan Suragan

School of Sciences and Humanities

Al Farabi Kazakh National University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	39
Journal	Mathematical Modelling of Natural Phenomena
Volume	13
Issue number	4
DOIs	https://doi.org/10.1051/mmnp/2018042
Publication status	Published - 2018

Keywords

Dirichlet sub-Laplacian
Green function
Quaternion Heisenberg group

ASJC Scopus subject areas

Modelling and Simulation
Applied Mathematics

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10.1051/mmnp/2018042

Cite this

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abstract = "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.",

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AU - Sabitbek, Bolys

AU - Suragan, Durvudkhan

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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

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UR - https://www.scopus.com/pages/publications/85053629763#tab=citedBy

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DO - 10.1051/mmnp/2018042

M3 - Article

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SN - 0973-5348

VL - 13

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

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ER -

On green functions for Dirichelet sub-Laplacians on a Quaternion Heisenberg group

Abstract

Keywords

ASJC Scopus subject areas

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