列维方程和局部最大值特性

arXiv - MATH - Complex Variables Pub Date : 2024-09-09 DOI:arxiv-2409.05776

Giuseppe Della Sala, Giuseppe Tomassini

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引用次数: 0

摘要

本文旨在研究在$\mathbb C^2$中强伪凸域$\Omega$上的列维算子的迪里赫特问题解的水平集。这些解一般都是非光滑的，它们的水平集的几何性质是通过它们与 $b\Omega$ 的交点的船体来描述的，主要工具是 Slodkowski 提出的局部最大值性质（PJM，1988 年）。然后使用同样的技术来研究 $\mathbb C^2$ 中图形的完整列维算子的行为。

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Levi equation and local maximum property

The aim of the paper is to study the level sets of the solutions of Dirichlet problems for the Levi operator on strongly pseudoconvex domains $\Omega$ in $\mathbb C^2$. Such solutions are generically non smooth, and the geometric properties of their level sets are characterized by means of hulls of their intersections with $b\Omega$, using as main tool the local maximum property introduced by Slodkowski (PJM, 1988). The same techniques are then employed to study the behavior of the complete Levi operator for graphs in $\mathbb C^2$.

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arXiv - MATH - Complex Variables

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