On Hilbert, Riemann, Neumann and Poincare problems for plane quasiregular mappings

Abstract

Recall that the Hilbert (Riemann-Hilbert) boundary value problem for the Beltrami equations was recently solved for general settings in terms of nontangential limits and principal asymptotic values. Here it is developed a new approach making possible to obtain new results on tangential limits in multiply connected domains. It is shown that the spaces of the found solutions have the infinite dimension for prescribed families of Jordan arcs terminating in almost every boundary point. We give also applications of results obtained by us for the Beltrami equations to the boundary value problems of Dirichlet, Riemann, Neumann and Poincare for A-harmonic functions in the plane.