Book section
Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry
- Abstract:
- We study entire continuous viscosity solutions to fully nonlinear elliptic equations involving the conformal Hessian. We prove the strong comparison principle and Hopf Lemma for (non-uniformly) elliptic equations when one of the competitors is $C^{1,1}$. We obtain as a consequence a Liouville theorem for entire solutions which are approximable by $C^{1,1}$ solutions on larger and larger compact domains, and, in particular, for entire $C^{1,1}_{\rm loc}$ solutions: they are either constants or standard bubbles.
- Publication status:
- Accepted
- Peer review status:
- Reviewed (other)
Actions
Authors
Contributors
+ Chen, J
Role:
Editor
+ Lu, P
Role:
Editor
+ Lu, Z
Role:
Editor
+ Zhang, Z
Role:
Editor
Bibliographic Details
- Publisher:
- Springer Publisher's website
- Series:
- Progress in Mathematics
- Host title:
- Geometric Analysis: In Honor of Gang Tian's 60th Birthday
- Publication date:
- 2019-01-01
- Pubs id:
-
pubs:1004696
- URN:
-
uri:7bd8bd41-f39b-4cb7-af6f-af3827041c14
- UUID:
-
uuid:7bd8bd41-f39b-4cb7-af6f-af3827041c14
- Local pid:
- pubs:1004696
Item Description
- Keywords:
Terms of use
- Copyright date:
- 2019
If you are the owner of this record, you can report an update to it here: Report update to this record