  We prove regularity of solutions of the $\bar\partial$-problem in the
H\"older-Zygmund spaces of bounded, strongly $\mathbf C$-linearly convex
domains of class $C^{1,1}$. The proofs rely on a new, analytic characterization
of said domains which is of independent interest, and on techniques that were
recently developed by the first-named author to prove estimates for the
$\bar\partial$-problem on strongly pseudoconvex domains of class $C^2$.
