∂̄ -problem for an overdetermined system with two higher dimensional variables

Ricardo Abreu-Blaya, Juan Bory-Reyes

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Our main purpose is to describe necessary and sufficient conditions for the solvability of the ∂̄ -problem for biregular complex Clifford algebra valued functions of two higher dimensional variables in even dimensional Euclidean spaces. Since the biregular function theory falls naturally from the so-called isotonic Clifford analysis, the main idea of the proof is based on the notion of biregular-conjugate harmonic functions to be introduced here. Besides, whenever the ∂̄ -problem is solvable, we give the general solution of it in a quite explicit form.

Original languageEnglish
Pages (from-to)579-586
Number of pages8
JournalArchiv der Mathematik
Volume97
Issue number6
DOIs
StatePublished - Dec 2011
Externally publishedYes

Keywords

  • Clifford analysis
  • Conjugate harmonic functions
  • ∂̄-problem

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