On differential properties of functions of bounded variation

It is established that Karagulyan??s exact estimate of the divergence rate of strong integral means of summable functions is extendable to strong means of additive functions of intervals having bounded variation. Furthermore, it is proved that each function defined on [0, 1] ⁿ with bounded variation in the sense of Hardy has a strong gradient at almost every point (this strengthens the corresponding result of Burkill and Haslam-Jones on the differentiability almost everywhere), whereas the same is not true for functions with bounded variation in the sense of Arzela.     

Boundary Value Problems of the Theory of Analytic Functions with Displacements

Integral representations are constructed for functions holomorphic in a strip. Using these representations an effective solution of Carleman type problem is given for a strip.     

The contact problem for a piecewise-homogeneous plane with a semi-infinite inclusion

A piecewise-homogenous elastic plate, reinforced with a semi-infinite inclusion, which intersects the interface at a right angle and is loaded with shear forces is considered. The contact stresses along the contact line are determined and the behaviour of the contact stresses in the neighbourhood of singular points is established. Using methods of the theory of analytical functions and integral transformations the problem is reduced to a system of singular integro-differential equations on the semi-axis. The solution is presented in explicit form.     

Solution of an infinite system of algebraic equations

A system of infinite algebraic equations is solved explicitly using a Carleman-type problem.     

The contact problem for a piecewise-homogeneous plane with a finite inclusion

A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite inclusion, which meets the interface at a right angle and is loaded with shear forces, is considered. The contact stresses along the contact line are determined, and the behaviour of the contact stresses in the neighbourhood of singular points is established. By using the methods of the theory of analytic functions, the problem is reduced to a singular integro-differential equation in a finite section. Using an integral transformation, a Riemann problem is obtained, the solution of which is presented in explicit form.