  We derive a new homotopy formula for a strictly pseudoconvex domain of $C^2$
boundary in ${\mathbf C}^n$ by using a method of Lieb and Range and obtain
estimates in Lipschitz spaces for the homotopy operators. For $r>1$ and $q>0$,
we obtain a $\Lambda_{r+{1}/{2}}$ solution $u$ to $\overline\partial u=f$ for
$\overline\partial$-closed $(0,q)$ forms $f$ of class $\Lambda_{r}$ on the
domain. We apply the estimates to obtain boundary regularities of $\mathcal
D$-solutions for a domain in the Levi-flat Euclidean space.
