IJPAM: Volume 81, No. 3 (2012)

SOLVABILITY CONDITIONS OF THE NEUMANN BOUNDARY
VALUE PROBLEM FOR THE BIHARMONIC
EQUATION IN THE UNIT BALL

Valery Karachik$^1$, Batirkhan Turmetov$^2$, Aygerim Bekaeva$^3$
$^1$Department of Mathematical Analysis
South Ural State University
Chelyabinsk 454080, RUSSIA
$^{2,3}$Department of Mathematics
International Kazakh-Turkish University
(named after A. Yasawi)
Turkestan, 161200, REPUBLIC OF KAZAKHSTAN


Abstract. The necessary and sufficient solvability condition of the Neumann boundary value problem for the inhomogeneous biharmonic equation in the unit ball is obtained. Solution with polynomial boundary data is constructed.

Received: August 31, 2012

AMS Subject Classification: 35J40, 35J05

Key Words and Phrases: Neumann boundary value problem, biharmonic equation, polynomial solution

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 3