2012/02/05 by S. V. Gryshchuk, Gryshchuk, S. V., С. А. Плакса +2
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Holomorphic and Operator Theory #math.CV #msc:30G35 #msc:31A30
paper · pdf · doi:10.48550/arxiv.1202.0993
arxiv created 2012/02/05 · arxiv updated 2012/02/07
We consider a two-dimensional commutative algebra B over the field of complex numbers. The algebra B is associated with the biharmonic equation. For monogenic functions with values in B, we consider a Schwartz-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 Schwartz-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.