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

Viet-Anh Nguyen; El Hassan Youssfi

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

Complex Variables 2007-05-23 v1

Authors: Viet-Anh Nguyen , El Hassan Youssfi

Abstract

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 $p.$

Keywords

cauchy-riemann equation convex domains lipschitz estimates bar partial equation optimal regularity

Cite

@article{arxiv.math/0611398,
  title  = {Optimal Lipschitz Estimates for the $\bar\partial$ equation on a class of convex domains},
  author = {Viet-Anh Nguyen and El Hassan Youssfi},
  journal= {arXiv preprint arXiv:math/0611398},
  year   = {2007}
}

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