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

On a decomposition of regular domains into John domains with uniform constants