论文标题
$ \ bar \ partial $ -neumann问题的最大估计值
Maximal Estimates for the $\bar\partial$-Neumann Problem on Non-pseudoconvex domains
论文作者
论文摘要
众所周知，对于$ \ bar \ partial $ -Neumann问题而言，椭圆估计失败。取而代之的是，人们所希望的最好的是在每个方向上都可以通过相关的Dirichlet表格来估算衍生物，并且当发生这种情况时，我们说$ \ bar \ partial $ -neumann问题可以满足最大估计。在伪共子案例中，Derridj（$（0,1）$ - 表单）和Ben Moussa（$（0，q）$ - $ q \ geq 1 $）得出了最大估计的必要和足够的几何条件。在本文中，我们探讨了在非预峰案例中最大估计的必要条件和足够条件。我们还讨论了必要的条件和足够条件何时同意并提供例子。我们的结果包含了伪共子病例的早期已知结果。
It is well known that elliptic estimates fail for the $\bar\partial$-Neumann problem. Instead, the best that one can hope for is that derivatives in every direction but one can be estimated by the associated Dirichlet form, and when this happens, we say that the $\bar\partial$-Neumann problem satisfies maximal estimates. In the pseudoconvex case, a necessary and sufficient geometric condition for maximal estimates has been derived by Derridj (for $(0,1)$-forms) and Ben Moussa (for $(0,q)$-forms when $q\geq 1$). In this paper, we explore necessary conditions and sufficient conditions for maximal estimates in the non-pseudoconvex case. We also discuss when the necessary conditions and sufficient conditions agree and provide examples. Our results subsume the earlier known results from the pseudoconvex case.
