Potential Type Operators on Curves with Vorticity Points

V. Rabinovich

Abstract: 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 $\nu(y)$ to the curve $\Gamma$ does not have a limit at the singular points and, moreover, $\nu(y)$ 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 $L_{p,w}(\Gamma,\C^n)$ where $p \in (1,\infty)$ and $w$ is a weight satisfying the Muckenhoupt condition.

Keywords: potential operators, Fredholmness, essential spectrum

Classification (MSC2000): 31A10

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