  We derive a decomposition result for regular, two-dimensional domains into
John domains with uniform constants. We prove that for every simply connected
domain $\Omega \subset {\Bbb R}^2$ with $C^1$-boundary there is a corresponding
partition $\Omega = \Omega_1 \cup \ldots \cup \Omega_N$ with $\sum_{j=1}^N
\mathcal{H}^1(\partial \Omega_j \setminus \partial \Omega) \le \theta$ such
that each component is a John domain with a John constant only depending on
$\theta$. The result implies that many inequalities in Sobolev spaces such as
Poincar\'e's or Korn's inequality hold on the partition of $\Omega$ for uniform
constants, which are independent of $\Omega$.
