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

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. © 2011 Springer Basel AG.

Año de publicación:

2011

Keywords:

• ∂̄-problem
• Clifford analysis
• Conjugate harmonic functions

Fuente:

scopus