Valery V. Karachik, “Polynomial solutions to Dirihlet boundary value problem for the <nobr>$3$</nobr>-harmonic equation in a ball”, J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 4,Pages <nobr>527

This article is cited in 9 papers

Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a ball

Valery V. Karachik

South Ural State University, Chelyabinsk, Russia

Abstract: Polynomial solution to Dirihlet boundary value problem for the nonhomogeneous $3$-harmonic equation in a ball with polynomial right-hand side and polynomial boundary data is found.

Keywords: $3$-harmonic equation, Almansi decomposition, harmonic polynomials, Dirihlet boundary value problem, polynomial solutions.

UDC: 513.88

Received: 21.03.2012
Received in revised form: 01.04.2012
Accepted: 21.06.2012