Schwartz-type integrals in a biharmonic plane
Complex Variables
2012-02-07 v1
Abstract
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.
Cite
@article{arxiv.1202.0993,
title = {Schwartz-type integrals in a biharmonic plane},
author = {S. V. Gryshchuk and S. A. Plaksa},
journal= {arXiv preprint arXiv:1202.0993},
year = {2012}
}