Optimal Lipschitz Estimates for the $\bar\partial$ equation on a class   of convex domains
  In this paper, we consider the Cauchy-Riemann equation $\bar\partial u= f$ in a new class of convex domains in $\C^n.$ We prove that under $L^p$ data, we can choose a solution in the Lipschitz space $\Lambda_{\alpha},$ where $\alpha$ is an optimal positive number given explicitly in terms of $p.$ 
Viet-Anh Nguyen and El Hassan Youssfi