Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations
We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very clo...
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| Format: | Journal article |
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Springer Verlag
2017
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| _version_ | 1797059071276220416 |
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| author | Li, Y Nguyen, L |
| author_facet | Li, Y Nguyen, L |
| author_sort | Li, Y |
| collection | OXFORD |
| description | We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single standard bubble in a universal positive distance around each blow-up point, and (iii) the heights of these bubbles are comparable by a universal factor. As an application of this result, we establish a quantitative Liouville theorem. |
| first_indexed | 2024-03-06T19:59:04Z |
| format | Journal article |
| id | oxford-uuid:26a62566-e56c-4010-99c2-2bfaeeb7a5b2 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:59:04Z |
| publishDate | 2017 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:26a62566-e56c-4010-99c2-2bfaeeb7a5b22022-03-26T12:02:11ZSymmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:26a62566-e56c-4010-99c2-2bfaeeb7a5b2Symplectic Elements at OxfordSpringer Verlag2017Li, YNguyen, LWe establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single standard bubble in a universal positive distance around each blow-up point, and (iii) the heights of these bubbles are comparable by a universal factor. As an application of this result, we establish a quantitative Liouville theorem. |
| spellingShingle | Li, Y Nguyen, L Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations |
| title | Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations |
| title_full | Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations |
| title_fullStr | Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations |
| title_full_unstemmed | Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations |
| title_short | Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations |
| title_sort | symmetry quantitative liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations |
| work_keys_str_mv | AT liy symmetryquantitativeliouvilletheoremsandanalysisoflargesolutionsofconformallyinvariantfullynonlinearellipticequations AT nguyenl symmetryquantitativeliouvilletheoremsandanalysisoflargesolutionsofconformallyinvariantfullynonlinearellipticequations |