Optimal Lipschitz Estimates for the $\bar\partial$ equation on a class of convex domains

Nguyen, Viet-Anh; Youssfi, El Hassan

Optimal Lipschitz Estimates for the $\bar\partial$ equation on a class of convex domains

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Description

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 $Λ_α,$ where $α$ is an optimal positive number given explicitly in terms of $p.$