On subsolutions and concavity for fully nonlinear elliptic equations
Subsolutions and concavity play critical roles in classical solvability, especially a priori estimates, of fully nonlinear elliptic equations. Our first primary goal in this paper is to explore the possibility to weaken the concavity condition. The second is to clarify relations between weak notions...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-03-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2023-0116 |
| _version_ | 1797219159262625792 |
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| author | Guan Bo |
| author_facet | Guan Bo |
| author_sort | Guan Bo |
| collection | DOAJ |
| description | Subsolutions and concavity play critical roles in classical solvability, especially a priori estimates, of fully nonlinear elliptic equations. Our first primary goal in this paper is to explore the possibility to weaken the concavity condition. The second is to clarify relations between weak notions of subsolution introduced by Székelyhidi and the author, respectively, in attempt to treat equations on closed manifolds. More precisely, we show that these weak notions of subsolutions are equivalent for equations defined on convex cones of type 1 in the sense defined by Caffarelli, Nirenberg and Spruck. |
| first_indexed | 2024-04-24T12:29:13Z |
| format | Article |
| id | doaj.art-09e101e6a0be469997d3bd0646309dbc |
| institution | Directory Open Access Journal |
| issn | 2169-0375 |
| language | English |
| last_indexed | 2024-04-24T12:29:13Z |
| publishDate | 2024-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-09e101e6a0be469997d3bd0646309dbc2024-04-08T07:35:24ZengDe GruyterAdvanced Nonlinear Studies2169-03752024-03-01241152810.1515/ans-2023-0116On subsolutions and concavity for fully nonlinear elliptic equationsGuan Bo0Department of Mathematics, Ohio State University, Columbus, OH43210, USASubsolutions and concavity play critical roles in classical solvability, especially a priori estimates, of fully nonlinear elliptic equations. Our first primary goal in this paper is to explore the possibility to weaken the concavity condition. The second is to clarify relations between weak notions of subsolution introduced by Székelyhidi and the author, respectively, in attempt to treat equations on closed manifolds. More precisely, we show that these weak notions of subsolutions are equivalent for equations defined on convex cones of type 1 in the sense defined by Caffarelli, Nirenberg and Spruck.https://doi.org/10.1515/ans-2023-0116fully nonlinear elliptic equations on riemannian manifoldsdirichlet problema priori estimatesconcavitysubsolutions35j1558j0535b45 |
| spellingShingle | Guan Bo On subsolutions and concavity for fully nonlinear elliptic equations Advanced Nonlinear Studies fully nonlinear elliptic equations on riemannian manifolds dirichlet problem a priori estimates concavity subsolutions 35j15 58j05 35b45 |
| title | On subsolutions and concavity for fully nonlinear elliptic equations |
| title_full | On subsolutions and concavity for fully nonlinear elliptic equations |
| title_fullStr | On subsolutions and concavity for fully nonlinear elliptic equations |
| title_full_unstemmed | On subsolutions and concavity for fully nonlinear elliptic equations |
| title_short | On subsolutions and concavity for fully nonlinear elliptic equations |
| title_sort | on subsolutions and concavity for fully nonlinear elliptic equations |
| topic | fully nonlinear elliptic equations on riemannian manifolds dirichlet problem a priori estimates concavity subsolutions 35j15 58j05 35b45 |
| url | https://doi.org/10.1515/ans-2023-0116 |
| work_keys_str_mv | AT guanbo onsubsolutionsandconcavityforfullynonlinearellipticequations |