A fundamental solution for a nonelliptic partial differential operator, II

Peter Greiner, Yutian LI

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)407-433
Number of pages27
JournalAnalysis and Applications
Volume16
Issue number3
DOIs
Publication statusPublished - 1 May 2018

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • fundamental solution
  • special functions
  • Subelliptic operator

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