  We generalize to intersection of strictly $c$ -convex domains in Stein
manifold, $ L^{r}-L^{s}$ and Lipschitz estimates for the solutions of the $
\bar \partial $ equation done by Ma and Vassiliadou for domains in $
{\mathbb{C}}^{n}.$ For this we use a Docquier-Grauert holomorphic retraction
plus the raising steps method I introduce earlier. This gives results in the
case of domains with low regularity, $ {\mathcal{C}}^{3},$ for their boundary.
