Riemann-Hilbert theory for problems with vanishing coefficients that arise in nonlinear hydrodynamics
Let a function \(a(t)\) be periodic on the real axis with the period \(2\pi \) and belonging to the space \(L^{\infty }\). Let \(a\geq 0\). At every point \(t\) either \(a\) is separated from zero at \(t\) or vanishes at \(t\). The authors consider the Riemann-Hilbert problem \(\Psi =a\Phi \), \(\left|t\right|=1\), with respect to the functions \(\Psi \) and \(\Phi \) analytic in the unit disc. The problem is considered in a class of Nevanlinna-Smirnov functions.
scientific article; zbMATH DE number 1895824
scientific article