∂̄-problem in domains of C ² in terms of hyper-conjugate harmonic functions

Abstract:

Given a Jordan domain of C 2, we consider the ∂̄-problem and establish a necessary and sufficient condition for its solvability in terms of the existence of hyper-conjugate harmonic functions, a notion coming from quaternionic analysis. Besides, whenever the ∂̄-problem is solvable we give its general solution in a quite explicit form. © 2012 Copyright Taylor and Francis Group, LLC.

Año de publicación:

2012

Keywords:

• Borel-Pompeiu formula
• ∂̄-problem
• Théodoresco operator
• Cauchy-Fueter operator
• hyper-conjugate harmonic functions

Fuente:

scopus