On fibering into analytic curves of the common boundary of two domains of holomorphy

An analogue of the Frobenius theorem is proved for the case of a continuous planar field. This leads to a proof that it is possible to fiber into analytic curves a $C^1$ smooth hypersurface in $\mathbf C^2$ on both sides of which lie domains of holomorphy. An example constructed of two domains of holomorphy with common boundary which does not contain analytic subsets.
Bibliography: 5 titles.