A note about Riemann boundary value problems on non-rectifiable curves

Abstract

In this article, the stability of Riemann boundary value problems (BVP) on some non-rectifiable Jordan curves Γ with Hausdorff dimension s > 1 is discussed. We find that for it is impossible for the solutions to Riemann BVPs to be stable for both jump functions and curves.

Dedicated to Professor Lu Jianke's 85th birthday.

Keywords:

• Riemann BVP
• Non-rectifiable curve
• Stability of Cauchy integral

AMS Subject Classifications: :

• 30E20
• 30E25

Acknowledgements

The author thanks DAAD for a visiting scholarship at the Department of Mathematics and Computer Sciences of the Free University Berlin in summer 2006. This research was also supported by the Foundation of Tianjin Municipal Education Commission (20050403).

Notes

Dedicated to Professor Lu Jianke's 85th birthday.