IJPAM: Volume 83, No. 1 (2013)



National Academy of Sciences of Ukraine
Tereshchenkivska Str. 3, 01601, Kiev, UKRAINE
Abstract. We consider the commutative algebra over the field of
complex numbers with the bases
satisfying the
conditions
,
. This algebra
is unique and it is associated with the biharmonic equation. We
consider monogenic functions (having the classic derivative in
domains of the biharmonic plane
, where
are
real) with values in
. For these functions, we
consider a Schwarz-type boundary value problem (associated with
the main biharmonic problem) for a half-plane and for a disk of
the biharmonic plane.
We obtain solutions in explicit forms by means of Schwarz-type
integrals and prove that the mentioned problem is solvable
unconditionally for a half-plane but it is solvable for a disk if
and only if a certain natural condition is satisfied.
Received: December 12, 2012
AMS Subject Classification: 30G35, 31A30
Key Words and Phrases: biharmonic equation, biharmonic algebra, biharmonic plane, monogenic function, Schwarz-type boundary value problem, biharmonic Schwarz integral
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DOI: 10.12732/ijpam.v83i1.13 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 1