Boundary value problems in the theory of analytic functions in Hölder classes on Riemann surfaces

1971 ◽  
Vol 26 (1) ◽  
pp. 117-192 ◽  
Author(s):  
E I Zverovich
Keyword(s):  
Boundary Value Problems ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Boundary Value ◽  
Hölder Classes ◽  
Holder Classes

scholarly journals Boundary Value Problems Governed by Superdiffusion in the Right Angle: Existence and Regularity

2018 ◽  
Vol 2018 ◽  
pp. 1-29
Author(s):  
Ramzet Dzhafarov ◽  
Nataliya Vasylyeva
Keyword(s):  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Boundary Value ◽  
Boundary Problems ◽  
Classical Solvability ◽  
Hölder Classes ◽  
The Right ◽  
Holder Classes

For α∈(1,2), we analyze a stationary superdiffusion equation in the right angle in the unknown u=u(x1,x2): Dx1αu+Dx2αu=f(x1,x2), where Dxα is the Caputo fractional derivative. The classical solvability in the weighted fractional Hölder classes of the associated boundary problems is addressed.

scholarly journals Generalized Analytic Functions in Higher Dimensions

2007 ◽  
Vol 14 (3) ◽  
pp. 581-595
Author(s):  
Wolfgang Tutschke
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Analytic Functions ◽  
Boundary Value ◽  
Higher Dimensions ◽  
Partial Differential ◽  
Generalized Analytic Functions ◽  
Linear Partial Differential Equations ◽  
Weakly Singular

Abstract Originally I. N. Vekua's theory of generalized analytic functions dealt only with linear systems of partial differential equations in the plane. The present paper shows why I. N. Vekua's ideas are also fruitful for the solution of linear and non-linear partial differential equations in higher dimensions. One of the highlights of the theory of generalized analytic functions in the plane is the reduction of boundary value problems for general (linear or nonlinear) equations to boundary value problems for holomorphic functions using the well-known weakly singular and strongly singular 𝑇- and П-operators, respectively. The present paper is mainly aimed at reducing boundary value problems in higher dimensions to boundary value problems for monogenic functions.

scholarly journals Stability of mathematical models of the main problems of the anisotropic theory of elasticity

2020 ◽  
Vol 30 (1) ◽  
pp. 112-124
Author(s):  
A.V. Yudenkov ◽  
A.M. Volodchenkov
Keyword(s):  
Boundary Value Problems ◽  
Analytic Functions ◽  
Boundary Value ◽  
Research Result ◽  
Theory Of Elasticity ◽  
Boundary Problems ◽  
Main Research ◽  
Contour Shape ◽  
Variable Function ◽  
Anisotropic Bodies

The boundary problems of the complex-variable function theory are effectively used while investigating equilibrium of homogeneous elastic mediums. The most complicated systems of the boundary value problems correspond to the case when an elastic body exhibits anisotropic properties. Anisotropy of the medium results in the drift of boundary conditions of the function that in general disrupts analyticity of the functions of interest. The paper studies systems of the boundary value problems with drift for analytic vectors corresponding to the primal elastic problems (first, second and mixed problems). Systems of analytic vectors with drift are reduced to equivalent systems of Hilbert boundary value problems for analytic functions with weak singularity integrators. The obtained general solution of the primal boundary value problems for the anisotropic theory of elasticity allows us to check the above problems for stability with respect to perturbations of boundary value conditions and contour shape. The research is relevant as there is necessity to apply approximate numerical methods to the boundary value problems with drift. The main research result comes to be a proof of stability of the systems of the vector boundary value problems with drift for analytic functions on the Hölder space corresponding to the primal problems of the elastic theory for anisotropic bodies in the case of change in the boundary value conditions and contour shape.

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