A fundamental solution for a nonelliptic partial differential operator, II

Peter Greiner; Yutian Li

doi:10.1142/S0219530516500196

A fundamental solution for a nonelliptic partial differential operator, II

Peter Greiner^*, Yutian Li

^*Corresponding author for this work

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

Abstract

Let Z denote the holomorphic tangential vector field to the generalized upper-half plane = {(z1,z) isin; ℂ²; Ρ = Im z 1 -|z|⁴ > 0}. In our terminology, t = Re z₁. Consider the ?b operator on the boundary of , D,Ⅎ = -1/2(ZZ + ZZ); note that Ⅎ is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution F to Ⅎ. Our approach is based on special functions and their properties.

Original language	English
Pages (from-to)	407-433
Number of pages	27
Journal	Analysis and Applications
Volume	16
Issue number	3
DOIs	https://doi.org/10.1142/S0219530516500196
Publication status	Published - 1 May 2018

Scopus Subject Areas

Analysis
Applied Mathematics

User-Defined Keywords

fundamental solution
special functions
Subelliptic operator

Access to Document

10.1142/S0219530516500196

Cite this

@article{383c899f712f43d7abedab87fd25fcf0,

title = "A fundamental solution for a nonelliptic partial differential operator, II",

abstract = "Let Z denote the holomorphic tangential vector field to the generalized upper-half plane = {(z1,z) isin; ℂ2; Ρ = Im z 1 -|z|4 > 0}. In our terminology, t = Re z1. Consider the ?b operator on the boundary of , D,Ⅎ = -1/2(ZZ + ZZ); note that Ⅎ is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution F to Ⅎ. Our approach is based on special functions and their properties.",

keywords = "fundamental solution, special functions, Subelliptic operator",

author = "Peter Greiner and Yutian Li",

note = "Publisher copyright: {\textcopyright} 2018 World Scientific Publishing Company",

year = "2018",

month = may,

day = "1",

doi = "10.1142/S0219530516500196",

language = "English",

volume = "16",

pages = "407--433",

journal = "Analysis and Applications",

issn = "0219-5305",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "3",

}

TY - JOUR

T1 - A fundamental solution for a nonelliptic partial differential operator, II

AU - Greiner, Peter

AU - Li, Yutian

PY - 2018/5/1

Y1 - 2018/5/1

N2 - Let Z denote the holomorphic tangential vector field to the generalized upper-half plane = {(z1,z) isin; ℂ2; Ρ = Im z 1 -|z|4 > 0}. In our terminology, t = Re z1. Consider the ?b operator on the boundary of , D,Ⅎ = -1/2(ZZ + ZZ); note that Ⅎ is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution F to Ⅎ. Our approach is based on special functions and their properties.

AB - Let Z denote the holomorphic tangential vector field to the generalized upper-half plane = {(z1,z) isin; ℂ2; Ρ = Im z 1 -|z|4 > 0}. In our terminology, t = Re z1. Consider the ?b operator on the boundary of , D,Ⅎ = -1/2(ZZ + ZZ); note that Ⅎ is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution F to Ⅎ. Our approach is based on special functions and their properties.

KW - fundamental solution

KW - special functions

KW - Subelliptic operator

UR - http://www.scopus.com/inward/record.url?scp=85000352180&partnerID=8YFLogxK

U2 - 10.1142/S0219530516500196

DO - 10.1142/S0219530516500196

M3 - Article

AN - SCOPUS:85000352180

VL - 16

SP - 407

EP - 433

JO - Analysis and Applications

JF - Analysis and Applications

SN - 0219-5305

IS - 3

ER -

A fundamental solution for a nonelliptic partial differential operator, II

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this