Potential Type Operators on Curves with Vorticity Points

  • Vladimir S. Rabinovich

    Escuelo Superior de Mat y Fis del IPN, México, D.f., Mexico


We study potential type operators on certain non-Lipschitz curves Γ\Gamma. The curves under consideration are locally Lyapunov except for a finite set FF of singular points. The normal vector v(y)v(y) to the curve Γ\Gamma does not have a limit at the singular points and, moreover, v(y)v(y) 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 Lp,w(Γ,Cn)L_{p,w} (\Gamma, \mathbb C^n) where p(1,)p \in (1, \infty) and ww 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. 1065–1081

DOI 10.4171/ZAA/928