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) limit...

This is a short survey paper based on the topics of the author’s research along with his collaborators. Main topics presented in the paper are on the regularity and rigidity theorems for the solutions of the elliptic differential equations. In particular, the author poses several open problems in these topics for further study. The paper contains six sections. Regularity theorems for the ellipt...

We consider the semi-flow defined by semi-linear parabolic equations in Lp-spaces and study the differentiable dependence on the initial data. Together with a spectral gap condition this implies existence of inertial manifolds in arbitrary space dimensions. The spectral gap condition is satisfied by the Laplace-Beltrami operator for a class of manifolds. The simplest examples are products of sp...

We consider general torsion components in three-dimensional Einstein-Cartan gravity, providing a geometrical interpretation for matter, and find new solutions of the corresponding equations Riemann curvature torsion. These geometries involve peculiar interplay between vector $(\beta_i)$ singlet $(\tau)$ irreducible which, under conditions, feature formal analogy with equation Beltrami fluid. In...

We study the existence of normalized homeomorphic solutions for degenerate Beltrami equation fz = μ(z )f in whole complex plane C , assuming that its measurable coefficient ), | ) |<1 a. e., has compact support and degeneration is controlled by tangential dilatation quotient KT μ (z z0) . show if bounded or finite mean oscillation dominants, satisfies Lehto type integral divergence condition...