3,795 research outputs found
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 Lavrentβev-Bitsadze equation in a mixed domain. A general mixed problem (according to Bitsadzeβs 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
Π€ΡΠ½ΠΊΡΠΈΠΈ, Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΠΎ ΠΡΠ³Π»ΠΈΡΡ
ΠΠΎΡΠΎΠ±ΠΈΠ΅ ΠΏΠΎΡΠ²ΡΡΠ΅Π½ΠΎ Π³ΠΈΠΏΠ΅ΡΠ°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΈΠΌ ΡΡΠ½ΠΊΡΠΈΡΠΌ, ΠΈΠ»ΠΈ ΡΡΠ½ΠΊΡΠΈΡΠΌ, Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΈΠΌ ΠΏΠΎ ΠΡΠ³Π»ΠΈΡΡ. ΠΠ»Ρ Π½ΠΈΡ
ΡΡΡΠΎΠΈΡΡΡ ΡΠ΅ΠΎΡΠΈΡ, Π°Π½Π°Π»ΠΎΠ³ΠΈΡ ΠΊΠ»Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅ΠΎΡΠΈΠΈ Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ½ΠΊΡΠΈΠΉ. Π£ΠΊΠ°Π·Π°Π½Ρ ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΠΊ ΡΠ»Π»ΠΈΠΏΡΠΈΡΠ΅ΡΠΊΠΈΠΌ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡΠΌ, ΠΏΠ»ΠΎΡΠΊΠΎΠΉ ΡΠ΅ΠΎΡΠΈΠΈ ΡΠΏΡΡΠ³ΠΎΡΡΠΈ ΠΈ Π³ΠΈΠ΄ΡΠΎΠΌΠ΅Ρ
Π°Π½ΠΈΠΊΠ΅. ΠΡΠ΅Π΄Π½Π°Π·Π½Π°ΡΠ°Π΅ΡΡΡ Π΄Π»Ρ ΠΈΠ½ΠΎΡΡΡΠ°Π½Π½ΡΡ
ΡΡΡΠ΄Π΅Π½ΡΠΎΠ² ΠΈ Π°ΡΠΏΠΈΡΠ°Π½ΡΠΎΠ² ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΏΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΡΡΠ΅ΠΉ ΡΠ½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅ΡΠΎ
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
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