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Zeitschrift für Analysis und ihre Anwendungen

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Volume 18, Issue 4, 1999, pp. 1065–1081
DOI: 10.4171/ZAA/928

Published online: 1999-12-31

Potential Type Operators on Curves with Vorticity Points

Vladimir S. Rabinovich[1]

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

We study potential type operators on certain non-Lipschitz curves $\Gamma$. The curves under consideration are locally Lyapunov except for a finite set $F$ of singular points. The normal vector $v(y)$ to the curve $\Gamma$ does not have a limit at the singular points and, moreover, $v(y)$ 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 $L_{p,w} (\Gamma, \mathbb C^n)$ where $p \in (1, \infty)$ and $w$ is a weight satisfying the Muckenhoupt condition.

Keywords: Potential operators, Fredholmness, essential spectrum

Rabinovich Vladimir S.: Potential Type Operators on Curves with Vorticity Points. Z. Anal. Anwend. 18 (1999), 1065-1081. doi: 10.4171/ZAA/928