TY - JOUR
T1 - A fundamental solution for a nonelliptic partial differential operator, II
AU - Greiner, Peter
AU - LI, Yutian
N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
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 -