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

Min Ku; Uwe Kähler; Paula Cerejeiras

Archivum Mathematicum (2012)

  • Volume: 048, Issue: 5, page 371-385
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Ku, Min, Kähler, Uwe, and Cerejeiras, Paula. "Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis." Archivum Mathematicum 048.5 (2012): 371-385. <http://eudml.org/doc/251370>.

@article{Ku2012,
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.},
author = {Ku, Min, Kähler, Uwe, Cerejeiras, Paula},
journal = {Archivum Mathematicum},
keywords = {Clifford analysis; polynomially generalized Bers–Vekua operator; Dirac operator; Clifford analysis; polynomially generalized Bers-Vekua operator; Dirac operator},
language = {eng},
number = {5},
pages = {371-385},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis},
url = {http://eudml.org/doc/251370},
volume = {048},
year = {2012},
}

TY - JOUR
AU - Ku, Min
AU - Kähler, Uwe
AU - Cerejeiras, Paula
TI - Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 5
SP - 371
EP - 385
AB - 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.
LA - eng
KW - Clifford analysis; polynomially generalized Bers–Vekua operator; Dirac operator; Clifford analysis; polynomially generalized Bers-Vekua operator; Dirac operator
UR - http://eudml.org/doc/251370
ER -

References

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  13. Min, K., Khäler, U., Daoshun, W., 10.1007/s00006-011-0308-2, Adv. Appl. Clifford Algebras 22 (2) (2012), 365–390. (2012) MR2930700DOI10.1007/s00006-011-0308-2
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