Approximation of functions from Hӧlder class by biharmonic Poisson integrals

Abstract

The biharmonic equation in Cartesian coordinates is considered for the case of the upper half-plane. The solution of such a fourth-order partial differential equation for given boundary conditions is represented in the form of an integral of the product of the function and the delta-shaped kernel, which in this paper plays the role of an approximating aggregate. In the paper, we found an exact equality for the upper bound of the deviation of Hölder class functions from the considered biharmonic Poisson operator in the uniform metric.