论文标题
$σ_K$ -Loewner-nirenberg问题的解决方案Annuli是本地Lipschitz，而不是可区分的
Solutions to the $σ_k$-Loewner-Nirenberg problem on annuli are locally Lipschitz and not differentiable
论文作者
论文摘要
我们以$ k \ geq 2 $显示本地Lipschitz粘度解决方案$σ_K$ -LOEWNER-NIRENBERG问题在给定的annulus $ \ {a <| x | <b \} $是$ c^{1，\ frac {1} {k}} _ {\ rm loc} $ in $ \ {a <| x | \ leq \ sqrt {ab} \} $和$ \ {\ sqrt {ab} \ leq | x | <b \} $，在$ | x |上有径向衍生物的跳跃= \ sqrt {ab} $。此外，对于任何$γ> \ frac {1} {k} $，该解决方案不是$ c^{1，γ} _ {\ rm loc} $。还建立了具有有限恒定边界值的Annuli上$σ_K$ -Yamabe问题解决方案的最佳规律性。
We show for $k \geq 2$ that the locally Lipschitz viscosity solution to the $σ_k$-Loewner-Nirenberg problem on a given annulus $\{a < |x| < b\}$ is $C^{1,\frac{1}{k}}_{\rm loc}$ in each of $\{a < |x| \leq \sqrt{ab}\}$ and $\{\sqrt{ab} \leq |x| < b\}$ and has a jump in radial derivative across $|x| = \sqrt{ab}$. Furthermore, the solution is not $C^{1,γ}_{\rm loc}$ for any $γ> \frac{1}{k}$. Optimal regularity for solutions to the $σ_k$-Yamabe problem on annuli with finite constant boundary values is also established.
