Begehr, Heinrich Dirichlet problems for the biharmonic equation. (English) Zbl 1136.31001 Gen. Math. 13, No. 2, 65-72 (2005). The author constructs an explicit solution of the biharmonic equation \[ (\partial_z \partial_{\overline z})^2 w = f \] in the unit disk \(\mathbb D =\{ z\in \mathbb C:\, | z|<1\}\) for two different sets of boundary conditions: (i)\(w=\varphi_0\), \(\partial_z \partial_{\overline z} w =\varphi_1\) on \(\partial \mathbb D\); (ii)\(w=\varphi_0\), \(\partial_{\overline z} w =\varphi_1\) on \(\partial \mathbb D\). Reviewer: Andrei Martinez Finkelshtein (Almeria) Cited in 8 Documents MSC: 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions Keywords:biharmonic equation; Dirichlet problem; unit disc of the complex plane PDFBibTeX XMLCite \textit{H. Begehr}, Gen. Math. 13, No. 2, 65--72 (2005; Zbl 1136.31001) Full Text: EuDML