Let

be the unit disc in $\mathbb{R}^2$ and

the set of continuous and $2\pi$-periodic real functions. The Dirichlet problem for the Laplace equation in the unit disc is stated as

for $\Delta=\dfrac{\partial^2}{\partial x^2}+\dfrac{\partial^2}{\partial y^2}$ the Laplace operator and some $f\in\mathcal{C}_{2\pi}(\mathbb{R})$ inducing $f\in\mathcal{C}(\partial D^2)$ by the parameterization $\mathbb{R}\longrightarrow\partial D^2$, $t\longmapsto(\cos t,\sin t)$