Solutions to the σk -Loewner-Nirenberg problem on annuli are locally Lipschitz and not differentiable

Author: 

Li, Y
Nguyen, L

Publication Date: 

26 January 2021

Journal: 

Journal of Mathematical Study

Last Updated: 

2021-04-05T18:29:16.66+01:00

Issue: 

2

Volume: 

54

DOI: 

10.4208/jms.v54n2.21.01

page: 

123-141

abstract: 

We show for k ≥ 2 that the locally Lipschitz viscosity solution to the σkLoewner-Nirenberg problem on a given annulus {a < |x| < b} is C
1,
1
k
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 > 1
k
. Optimal
regularity for solutions to the σk-Yamabe problem on annuli with finite constant
boundary values is also established.

Symplectic id: 

1105090

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article