Volume 1, Issue 6

We consider problems occurring in computing the Poisson integral when the point at which the integral is evaluated approaches the ball surface. Techniques are proposed enabling one to improve computation effectiveness.

The method of investigation of non-stationary boundary value problems of the theory of thermodiffusion using the Laplace integral transform is described. In the classical theory of elasticity this method was first used by V. Kupradze and the author.

This is the survey of the applications of the potential methods to the problems of continuum mechanics. Historical review, new results, prospects of the development are given.

The necessary and sufficient conditions are derived in order that a strong type weighted inequality be fulfilled in Orlicz classes for scalar and vector-valued maximal functions defined on homogeneous type space. A weak type problem with weights is solved for vector-valued maximal functions.

Oscillation criteria generalizing a series of earlier results are established for first order linear delay differential inequalities and equations.