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

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

2006-11-13

arxiv.org/abs/math/0611398v1

Ann. Fac. Sci. Toulouse, 12(2), (2003), 179--243

Mathematics

Complex Variables

Scientific paper

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 $p.$

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