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Volume 61 >>> № 5 SEPTEMBER — OCTOBER 2025
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DOI 10.34229/KCA2522-9664.25.5.12
UDC 519.8

A.M. Shutovskyi
Lesya Ukrainka Volyn National University, Lutsk, Ukraine,
 sh93ar@gmail.com


OPTIMIZATION PROPERTIES OF TAYLOR FORMULA
FOR TRIHARMONIC POISSON INTEGRAL

Abstract. The paper is devoted to the optimization problem on establishing a polynomial structure for solutions to polyharmonic equations. As a basis, a triharmonic equation in Cartesian coordinates with respect to three nontrivial boundary conditions is used. It is established that the solution to the boundary-value problem under consideration belongs to the class of positive operators. It is shown that the polynomial expansions for the boundary values of the triharmonic function close to the upper half-plane boundary give rise to the Taylor formula of the triharmonic Poisson integral. On the basis of this result, the existence of additional boundary conditions for solutions to the triharmonic equations in Cartesian coordinates is proved.

Keywords: triharmonic equation, optimization problem, upper half-plane, triharmonic Poisson integral, Taylor formula.


full text

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