C2中有限型伪凸域上∂∂∂方程的Sobolev估计和Hölder估计

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-05-13 DOI:10.1016/j.jmaa.2025.129638

Ziming Shi

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引用次数: 0

摘要

我们证明了一个同伦公式，它在所有（正指标）Sobolev和Hölder-Zygmund空间中对C2有限型伪凸域上的∂内生方程产生几乎明显的估计，扩展了Fefferman-Kohn (1988), Range（1990）和ham - nagel - stein（1992）的早期结果。我们的证明的主要新颖之处在于构造全纯支持函数，当参数变量位于定义域外的薄壳中时，该支持函数允许精确估计。

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Sobolev and Hölder estimates for the ∂‾ equation on pseudoconvex domains of finite type in C2

We prove a homotopy formula which yields almost sharp estimates in all (positive-indexed) Sobolev and Hölder-Zygmund spaces for the

\overline{\partial}

equation on pseudoconvex domains of finite type in

C^{2}

, extending the earlier results of Fefferman-Kohn (1988), Range (1990), and Chang-Nagel-Stein (1992). The main novelty of our proof is the construction of holomorphic support functions that admit precise estimates when the parameter variable lies in a thin shell outside the domain.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.