Revaz Bantsuri
abstract:
In the work the boundary value problems of the theory of analytic functions with
displacement are considered, namely: Carleman type problems with continuous and
unbounded coefficients for strip and circular ring, the Riemann--Hilbert
problems for doubly connected domains and discontinuous coefficients for ring.
The contact problems of the elasticity theory for unbounded (isotropic,
anisotropic and piecewise-homogeneous) domains with rectilinear boundaries with
elastic fastening are investigated. The boundary value problems of plane theory
of elasticity for anisotropic domains with cracks and inclusions are studied as
well as the third basic and mixed boundary value problems for doubly-connected
domains.
The methods of analytic functions, integral transformations and theory of
integral equations are applied. The solvability conditions of problems are
formulated and proved. New methods of factorization are developed and the
solutions of problems are represented in explicit form.
Mathematics Subject Classification: 43J05, 73C02, 74K20, 74M15
Key words and phrases: Boundary value problems, analytic functions, elasticity theory, contact problems, cracks and inclusions, Fourier transformations