We study potential type operators on certain non-Lipschitz curves . The curves under consideration are locally Lyapunov except for a finite set of singular points. The normal vector to the curve does not have a limit at the singular points and, moreover, may be an oscillating and rotating vector function in a neighborhood of the singular points. We establish a Fredholm theory of potential type operators in the spaces where and is a weight satisfying the Muckenhoupt condition.
Cite this article
Vladimir S. Rabinovich, Potential Type Operators on Curves with Vorticity Points. Z. Anal. Anwend. 18 (1999), no. 4, pp. 1065–1081DOI 10.4171/ZAA/928