On Green functions for Dirichlet sub-Laplacians on H-type groups

Nicola Garofalo; Michael Ruzhansky; Durvudkhan Suragan

doi:10.1016/j.jmaa.2017.03.031

On Green functions for Dirichlet sub-Laplacians on H-type groups

Nicola Garofalo
, Michael Ruzhansky
, Durvudkhan Suragan

Department of Mathematics

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

9 Citations (Scopus)

Abstract

We construct Green functions of Dirichlet boundary value problems for sub-Laplacians on certain unbounded domains of a prototype Heisenberg-type group (prototype H-type group, in short). We also present solutions in an explicit form of the Dirichlet problem for the sub-Laplacian with non-zero boundary datum on half-space, quadrant-space, etc., as well as in a strip.

Original language	English
Pages (from-to)	896-905
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	452
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2017.03.031
Publication status	Published - Aug 15 2017

Funding

The authors were supported in parts by the EPSRC grant EP/K039407/1 and by the Leverhulme Grant RPG-2014-02, as well as by the MESRK grant 5127/GF4. No new data was collected or generated during the course of this research.

Keywords

Dirichlet sub-Laplacian
Green function
Heisenberg-type group

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2017.03.031

Cite this

@article{f17cc02a67d349fdb095676f1d0ea380,

title = "On Green functions for Dirichlet sub-Laplacians on H-type groups",

abstract = "We construct Green functions of Dirichlet boundary value problems for sub-Laplacians on certain unbounded domains of a prototype Heisenberg-type group (prototype H-type group, in short). We also present solutions in an explicit form of the Dirichlet problem for the sub-Laplacian with non-zero boundary datum on half-space, quadrant-space, etc., as well as in a strip.",

keywords = "Dirichlet sub-Laplacian, Green function, Heisenberg-type group",

author = "Nicola Garofalo and Michael Ruzhansky and Durvudkhan Suragan",

note = "Funding Information: The authors were supported in parts by the EPSRC grant EP/K039407/1 and by the Leverhulme Grant RPG-2014-02, as well as by the MESRK grant 5127/GF4. No new data was collected or generated during the course of this research. Publisher Copyright: {\textcopyright} 2017 The Author(s)",

year = "2017",

month = aug,

day = "15",

doi = "10.1016/j.jmaa.2017.03.031",

language = "English",

volume = "452",

pages = "896--905",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - On Green functions for Dirichlet sub-Laplacians on H-type groups

AU - Garofalo, Nicola

AU - Ruzhansky, Michael

AU - Suragan, Durvudkhan

N1 - Funding Information: The authors were supported in parts by the EPSRC grant EP/K039407/1 and by the Leverhulme Grant RPG-2014-02, as well as by the MESRK grant 5127/GF4. No new data was collected or generated during the course of this research. Publisher Copyright: © 2017 The Author(s)

PY - 2017/8/15

Y1 - 2017/8/15

N2 - We construct Green functions of Dirichlet boundary value problems for sub-Laplacians on certain unbounded domains of a prototype Heisenberg-type group (prototype H-type group, in short). We also present solutions in an explicit form of the Dirichlet problem for the sub-Laplacian with non-zero boundary datum on half-space, quadrant-space, etc., as well as in a strip.

AB - We construct Green functions of Dirichlet boundary value problems for sub-Laplacians on certain unbounded domains of a prototype Heisenberg-type group (prototype H-type group, in short). We also present solutions in an explicit form of the Dirichlet problem for the sub-Laplacian with non-zero boundary datum on half-space, quadrant-space, etc., as well as in a strip.

KW - Dirichlet sub-Laplacian

KW - Green function

KW - Heisenberg-type group

UR - https://www.scopus.com/pages/publications/85015746069

UR - https://www.scopus.com/pages/publications/85015746069#tab=citedBy

U2 - 10.1016/j.jmaa.2017.03.031

DO - 10.1016/j.jmaa.2017.03.031

M3 - Article

AN - SCOPUS:85015746069

SN - 0022-247X

VL - 452

SP - 896

EP - 905

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On Green functions for Dirichlet sub-Laplacians on H-type groups

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this