On the Riemann–Hilbert Problem in the Domain with a Nonsmooth Boundary
V. Kokilashvili, Vakhtang Paatashvili · Georgian Mathematical Journal · 1997
Abstract The following Riemann–Hilbert problem is solved: find an analytical function Φ from the Smirnov class Ep (D), whose angular boundary values satisfy the condition Re[(a(t) + ib(t))Φ+ (t)] = ƒ(t). The boundary Γ of the domain D is assumed to be a piecewise smooth curve whose nonintersecting Lyapunov arcs form, with respect to D, the inner angles with values νkπ, 0 < νk ≤ 2.