(untitled) (Journal of Mathematical Study, 2021)
We show for k ≥ 2 that the locally Lipschitz viscosity solution to the σ_k-Loewner-Nirenberg problem on a given annulus {a < |x| < b} is C^1,1k _loc in each of {a < |x| ≤ ab} and {ab ≤ |x| < b} and has a jump in radial derivative across |x| = ab. Furthermore, the solution is not C^1,γ_loc for any γ > 1k. Optimal regularity for solutions to the σ_k-Yamabe problem on annuli with finite constant boundary values is also established.