Problem of Bitsadze-Samarskii type for second-order elliptic systems in the plane

For general elliptic equations Bitsadze-Samara has been the subject of numerous studies. In this paper, the problem is considered for functions analytic DouglisyesBelgorod State Universit

On Dirichlet-type problems for the Lavrentev-Bitsadze equation

The existence and uniqueness issues are discussed for several boundary value problems with Dirichlet data for the Lavrent’ev-Bitsadze equation in a mixed domain. A general mixed problem (according to Bitsadze’s terminology) is considered in which the Dirichlet data are relaxed on a hyperbolic region of the boundary inside a characteristic sector with vertex on the type-change interval. In particular, conditions are pointed out under which the problem is uniquely solvable for any choice of this vertexyesBelgorod State Universit

The Bitsadze-Samarskii problem for Douglis analytic functions

Studies the Bitsadze-Samarskii problem for Douglis analytic functions. Consideration Holder subspace of functions; Reduction of the problem to a system of singular integral equations; Role of a Cauchy type integral for the functionsyesBelgorod State Universit

The Schwarz problem for Douglis analytic functions

This paper considers the Schwarz problem that consists in finding a J-analytic function by its real part on the boundary. The Fredholm solvability of this problem is proved. The integral representation of J-analytic functions by Cauchy-type integrals with real density is obtainedyesBelgorod State Universit

The Hardy space of solutions to first-order elliptic systems

The space indicated in the title is introduced and studiedyesBelgorod State Universit

Функции, аналитические по Дуглису

Пособие посвящено гипераналитическим функциям, или функциям, аналитическим по Дуглису. Для них строится теория, аналогия классической теории аналитических функций. Указаны приложения к эллиптическим уравнениям, плоской теории упругости и гидромеханике. Предназначается для иностранных студентов и аспирантов математических специальностей университето

On representation of solutions of second order elliptic systems on the plane

The analogue of the Privalov theorem is established for solutions of elliptic systems of second order in Lipshitz domains. The corresponding result is also obtained with respect to the weighted H¨older spaces. The notion of conjugate functions to solutions of elliptic systems is introduced and representations formulas for them are received. For so called strengthen elliptic systems the class of degenerate solutions is describedyesBelgorod State Universit

To the theory of anisotropic plane elasticity

The Lame system of general anisotropic plane elasticity is considered. A representation of a general solution or the system through a so-called Douglis analytic functions is given. The cases of orthotropic and isotropic media are also consideredyesBelgorod State Universit

Hardy space of solutions of elliptic systems on the plane

The space indicated in the title is introduced and studiedyesBelgorod State Universit

On the index of the Dirichlet problem for elliptic systems on the plane

The article discusses partial differentiation, on the Dirichlet problem of plane for the elliptical equations. The article uses theorems and lemmas related to differential equations. The use of Jordan form of elliptical system and the Riemann-Hilbert problem, and criteria of the Lame system are given in the articleyesBelgorod State Universit