Potential type operators on curves with vorticity points (Q1969397)

The local spectrum and the essential spectrum of operators of the type of the double layer potential in the space \(L_{p,w}(\Gamma , {\mathbb C}^n)\) (for \(1<p<\infty \) and a weight \(w\) satisfying the Muckenhoupt condition) are investigated on the curve \(\Gamma \), which is locally Lyapunov except for a finite set of singular points. The normal vector \(\nu (y)\) may be an oscillating and rotating vector function in a neighbourhood of the singular points.