# Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis

## Min Ku, Uwe Kähler, and Paula Cerejeiras

Address: Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, P-3810-193 Aveiro, Portugal

E-mail:

kumin0844@163.com

kumin0844@gmail.com

ukaehler@ua.pt

pceres@ua.pt

Abstract: In this paper a class of polynomially generalized Vekua–type equations and of polynomially generalized Bers–Vekua equations with variable coefficients defined in a domain of Euclidean space are discussed. Using the methods of Clifford analysis, first the Fischer–type decomposition theorems for null solutions to these equations are obtained. Then we give, under some conditions, the solutions to the polynomially generalized Bers–Vekua equation with variable coefficients. Finally, we present the structure of the solutions to the inhomogeneous polynomially generalized Bers–Vekua equation.

AMSclassification: primary 30G35; secondary 32A25, 35C10.

Keywords: Clifford analysis, polynomially generalized Bers–Vekua operator, Dirac operator.

DOI: 10.5817/AM2012-5-371