# On the solution of the inhomogeneous polyharmonic equation and the inhomogeneous helmholtz equation

@article{Karachik2010OnTS, title={On the solution of the inhomogeneous polyharmonic equation and the inhomogeneous helmholtz equation}, author={V. Karachik and N. Antropova}, journal={Differential Equations}, year={2010}, volume={46}, pages={387-399} }

We present formulas that simplify finding the solutions of the Poisson equation, the inhomogeneous polyharmonic equation, and the inhomogeneous Helmholtz equation in the case of a polynomial right-hand side. They are based on the representation of an analytic function by harmonic functions. The resulting formulas remain valid for some analytic right-hand sides for which the corresponding operator series converge.

#### 15 Citations

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