@Article{JMS-54-2,
author = {Yanyan, Li and Nguyen, Luc},
title = {Solutions to the $\sigma_k$-Loewner-Nirenberg Problem on Annuli are Locally Lipschitz and Not Differentiable},
journal = {Journal of Mathematical Study},
year = {2021},
volume = {54},
number = {2},
pages = {123--141},
abstract = {<p style="text-align: justify;">We show for $k \geq 2$ that the locally Lipschitz viscosity solution to the $\sigma_k$-Loewner-Nirenberg problem on a given annulus $\{a &lt; |x| &lt; b\}$ is $C^{1,\frac{1}{k}}_{\rm loc}$ in each of $\{a &lt; |x| \leq \sqrt{ab}\}$ and $\{\sqrt{ab} \leq |x| &lt; b\}$ and has a jump in radial derivative across $|x| = \sqrt{ab}$. Furthermore, the solution is not $C^{1,\gamma}_{\rm loc}$ for any $\gamma &gt; \frac{1}{k}$. Optimal regularity for solutions to the $\sigma_k$-Yamabe problem on annuli with finite constant boundary values is also established.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v54n2.21.01},
url = {https://global-sci.com/article/87670/solutions-to-the-sigma-k-loewner-nirenberg-problem-on-annuli-are-locally-lipschitz-and-not-differentiable}
}