On the Hilbert problem for semi-linear Beltrami equations

The presented paper is devoted to the study of well-known Hilbert boundary-value problem for semi-linear Beltrami equations with arbitrary boundary data that are measurable respect logarithmic capacity. Namely, we prove here corresponding results on existence, regularity, and representation its nonclassical solutions a geometric interpretation values as angular (along nontangential paths) limits in comparison classical approach PDE. For this purpose, apply completely continuous operators by Ahlfors–Bers, first all obtain equations, generally speaking no conditions, then derive their through Vekua-type so-called generalized analytic functions sources. Besides, similar Poincaré directional derivatives and, particular, Neumann Poisson type. obtained applied some problems mathematical physics describing such phenomena diffusion physical chemical absorption, plasma states, stationary burning anisotropic inhomogeneous media.