Journal title
Journal of Mathematical Study
DOI
10.4208/jms.v54n2.21.01
Issue
2
Volume
54
Last updated
2023-12-19T14:23:06.14+00:00
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.
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
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Publication type
Journal Article
Publication date
26 Jan 2021