Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry
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 theore...
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| Other Authors: | |
| Format: | Book section |
| Language: | English |
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Springer
2020
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| _version_ | 1826312249485033472 |
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| author | Li, Y Nguyen, L Wang, B |
| author2 | Chen, J |
| author_facet | Chen, J Li, Y Nguyen, L Wang, B |
| author_sort | Li, Y |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T08:26:17Z |
| format | Book section |
| id | oxford-uuid:7bd8bd41-f39b-4cb7-af6f-af3827041c14 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:26:17Z |
| publishDate | 2020 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:7bd8bd41-f39b-4cb7-af6f-af3827041c142024-02-19T14:16:32ZTowards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometryBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:7bd8bd41-f39b-4cb7-af6f-af3827041c14EnglishSymplectic Elements at OxfordSpringer2020Li, YNguyen, LWang, BChen, JLu, PLu, ZZhang, ZWe 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. |
| spellingShingle | Li, Y Nguyen, L Wang, B Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry |
| title | Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry |
| title_full | Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry |
| title_fullStr | Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry |
| title_full_unstemmed | Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry |
| title_short | Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry |
| title_sort | towards a liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry |
| work_keys_str_mv | AT liy towardsaliouvilletheoremforcontinuousviscositysolutionstofullynonlinearellipticequationsinconformalgeometry AT nguyenl towardsaliouvilletheoremforcontinuousviscositysolutionstofullynonlinearellipticequationsinconformalgeometry AT wangb towardsaliouvilletheoremforcontinuousviscositysolutionstofullynonlinearellipticequationsinconformalgeometry |