Some Asymptotic Properties of Solutions to Triharmonic Equations

The author considers an optimization problem for the triharmonic equation under specific boundary conditions. As a result, the triharmonic Poisson integral is constructed in Cartesian coordinates for the upper half-plane. The asymptotic properties of this operator on Lipschitz classes in a uniform metric are analyzed. An exact equality is found for the upper bound of the deviation of the Lipschitz class functions from the triharmonic Poisson integral defined in Cartesian coordinates for the upper half-plane in the metric of space C. The results obtained in the article demonstrate how the methods of approximation theory relate to the principles of the optimal decision theory.