On estimates for the ${\displaystyle \bar{\mathrm{\partial }}}$ equation in Stein manifolds

We generalize to intersection of strictly $c$ -convex domains in Stein manifold, $L^r-L^s$ and Lipschitz estimates for the solutions of the $\bar{\mathrm{\partial }}$ equation done by Ma and Vassiliadou for domains in ${\mathbb{C}}^n\mathrm{.}$ 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.