  It is quite well known that Korn's inequality is true on all John domains. We
are interested in the converse implication under assumption of so called
separation condition of the domain. Our result implies that in a simply
connected planar domain the Korn's inequality holds if and only if the domain
is John. In particular, we obtain the equivalence of Korn's inequality, Babu\v
ska-Aziz inequality and Friedrich's inequality in simply connected planar
domains.
