Generalized monogenic functions satisfying differential equations with anti-monogenic right-hand sides on Clifford algebras depending on parameters

Abstract

The equation Du = F(x, u) in Clifford algebras depending on parameters is considered, where D is the Cauchy–Riemann operator. A sufficient condition for the right-hand side of the equation to be anti-monogenic is given. The given criterion enables the construction of anti-monogenic functions in Clifford algebras depending on parameters and yields interior L _p -estimates as well. The results provide generalizations of those in Tutschke and Yüksel (1999) [W. Tutschke and U. Yüksel, Generalized Monogenic Functions Satisfying Differential Equations with Anti-Monogenic Right-Hand Sides, ISAAC Series, Vol. 6, Kluwer Academic Publishers, Dordrecht, 1999, pp. 263–270].

Keywords:

• Clifford algebras depending on parameters
• anti-monogenic functions
• generalized monogenic functions
• transition matrix
• interior L _p estimates

AMS Subject Classifications::

• 30G35
• 35A08
• 45E05

Acknowledgements

I would like to express my sincere gratitude to Stefania Marcantognini, María Dolores Morán, Alfredo Rios and Wolfgang Tutschke for reading the manuscript and suggesting various improvements.