Solutions to the σk-Loewner-Nirenberg Problem on Annuli are Locally Lipschitz and Not Differentiable

IF 0.8 4区数学

数学研究 Pub Date : 2020-01-13 DOI:10.4208/JMS.V54N2.21.01

Yanyan Li, Luc Nguyen

引用次数: 12

Abstract

We show for $k \geq 2$ that the locally Lipschitz viscosity solution to the $\sigma_k$-Loewner-Nirenberg problem on a given annulus $\{a \frac{1}{k}$. Optimal regularity for solutions to the $\sigma_k$-Yamabe problem on annuli with finite constant boundary values is also established.

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环uli上σk-Loewner-Nirenberg问题的解是局部Lipschitz且不可微的

对于$k\geq2$，我们证明了给定环空$\｛a\frac｛1｝｛k｝$上$\sigma_k$-Loewner-Nirenberg问题的局部Lipschitz粘性解。建立了有限常边值环上$\sigma_k$-Yamabe问题解的最优正则性。

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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来源期刊

数学研究 MATHEMATICS-

自引率

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发文量

1109

期刊介绍： Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics.