Zigzags and Spirals in Boundary-Value Problems

Abstract

© 2019, Allerton Press, Inc. The notice is dealing with contour integrals over non-smooth paths and their applications for solving of boundary-value problems. There is established that solvability of the Riemann boundary-value problem on non-smooth arc essentially depends on the type of its non-smoothness: on a zigzag-like arc we obtain the same picture of solvability as on smooth arcs, but on spiral-like arcs the number of solutions depends on geometry of the spiral.