Criteria for monogenicity of Clifford algebra-valued functions on fractal domains

Abstract:

Suppose that Ω is a bounded domain with fractal boundary Γ in ℝn+1 and let ℝ0,n be the real Clifford algebra constructed over the quadratic space ℝn. Furthermore, let U be a ℝ0,n-valued function harmonic in Ω and Hölder-continuous up to Γ. By using a new Clifford Cauchy transform for Jordan domains in ℝn+1 with fractal boundaries, we give necessary and sufficient conditions for the monogenicity of U in terms of its boundary value u = U{pipe}Γ. As a consequence, the results of Abreu Blaya et al. (Proceedings of the 6th International ISAAC Congress Ankara, 167- 174, World Scientific) are extended, which require Γ to be Ahlfors-David regular. © 2010 Springer Basel AG.

Año de publicación:

2010

Keywords:

• Clifford analysis
• Cauchy transform
• Cauchy-Riemann operator

Fuente:

scopus