Type Of Integral Operators Research Articles

Regularized asymptotic solutions of the initial problem for the system of integro-partial differential equations

The Lomov regularization method [1] is generalized to integro-partial differential equations. It turns out that the regularization procedure essentially depends on the type of integral operator. The case in which the upper limit of the integral is not the differentiation variable is the most difficult one. It is not considered in the present paper. Only the case in which the upper limit of the integral operator coincides with the differentiation variable is studied. For such problems, an algorithm for constructing regularized asymptotics is developed.

The weighted norm inequalities of integral operators with special types of kernels

In this paper, the weighted norm inequalities of the following special type of integral operators are investigated:where or . In particular, those established by E. T. Copson, Hardy-Littlewood-Pólya, S. Lai, N. Levinson, E. R. Love, B. G. Pachpatte and Yang-Hwang will be derived.

Exact solutions to some external mixed problems in potential theory

A new and elegant procedure is proposed for the solution of mixed potential problems in a half-space with a circular line of division of boundary conditions. The approach is based on a new type of integral operators with special properties. Two general external problems are solved; i) An arbitrary potential is specified at the boundary outside a circle, and its normal derivative is zero inside; ii) An arbitrary normal derivative is given outside the circle, and be potential is zero inside. Several illustrative examples are considered. Certain methods of application of the proposed technique to the solution of a few complex problems are also discussed.