Lomako T. To the theory of extremal problems for mappings with finite distortion

The main results of the dissertation are following: a series of theorems on convergence, normality and compactness for new classes of regular solutions to the degenerate Beltrami equations with constraints of the integral and set-theoretic types for the complex coefficient; variations and necessary conditions of extremum for above classes; theorems on the local behavior for mappings with finite distortion under constraints of the integral type; the applications to the existence and representation of solutions with logarithmic singularities one of the main equations of mathematical physics; a precise estimation of the area of the image of disks under mappings of finite distortion with locally integrable dilatations.