$$\mathbb{R}^2$$中外部域上的准共形映射和伯恩斯坦类型定理

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-31 DOI:10.1007/s00526-024-02808-3

Dongsheng Li, Rulin Liu

引用次数: 0

摘要

我们建立了在$\mathbb {R}^2$外部域上的 K-quasiconformal 映射的赫尔德估计和无穷远处的渐近行为。因此，我们证明了在$\mathbb {R}^2$ 中二阶全非线性均匀椭圆方程的外部伯恩斯坦类型定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Quasiconformal mappings and a Bernstein type theorem over exterior domains in $$\mathbb {R}^2$$

We establish the Hölder estimate and the asymptotic behavior at infinity for K-quasiconformal mappings over exterior domains in $\mathbb {R}^2$. As a consequence, we prove an exterior Bernstein type theorem for fully nonlinear uniformly elliptic equations of second order in $\mathbb {R}^2$.

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.