On Singular Liouville Equations and Systems
We consider some singular Liouville equations and systems motivated by uniformization problems in a non-smooth setting, as well as from models in mathematical physics. We will study the existence of solutions from a variational point of view, using suitable improvements of the Moser–Trudinger inequa...
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| Format: | Article |
| Language: | English |
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De Gruyter
2017-02-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2016-6013 |
| _version_ | 1811280145827233792 |
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| author | Malchiodi Andrea |
| author_facet | Malchiodi Andrea |
| author_sort | Malchiodi Andrea |
| collection | DOAJ |
| description | We consider some singular Liouville equations and systems motivated by uniformization problems in a non-smooth setting, as well as from models in mathematical physics. We will study the existence of solutions from a variational point of view, using suitable improvements of the Moser–Trudinger inequality. These reduce the problem to a topological one by studying the concentration property of conformal volume, which will be constrained by the functional inequalities of geometric flavour. We will mainly describe some common strategies from the papers [11, 12, 20] in simple situations to give an idea to the non-expert reader about the general methods we use. |
| first_indexed | 2024-04-13T01:08:17Z |
| format | Article |
| id | doaj.art-eadb135010524170b687d38f13294dc8 |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-13T01:08:17Z |
| publishDate | 2017-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-eadb135010524170b687d38f13294dc82022-12-22T03:09:16ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752017-02-0117111113810.1515/ans-2016-6013On Singular Liouville Equations and SystemsMalchiodi Andrea0Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy We consider some singular Liouville equations and systems motivated by uniformization problems in a non-smooth setting, as well as from models in mathematical physics. We will study the existence of solutions from a variational point of view, using suitable improvements of the Moser–Trudinger inequality. These reduce the problem to a topological one by studying the concentration property of conformal volume, which will be constrained by the functional inequalities of geometric flavour. We will mainly describe some common strategies from the papers [11, 12, 20] in simple situations to give an idea to the non-expert reader about the general methods we use.https://doi.org/10.1515/ans-2016-6013geometric pdessingular liouville equationvariational methodsmin-max schemes35b33 53a30 53c21 81t13 |
| spellingShingle | Malchiodi Andrea On Singular Liouville Equations and Systems Advanced Nonlinear Studies geometric pdes singular liouville equation variational methods min-max schemes 35b33 53a30 53c21 81t13 |
| title | On Singular Liouville Equations and Systems |
| title_full | On Singular Liouville Equations and Systems |
| title_fullStr | On Singular Liouville Equations and Systems |
| title_full_unstemmed | On Singular Liouville Equations and Systems |
| title_short | On Singular Liouville Equations and Systems |
| title_sort | on singular liouville equations and systems |
| topic | geometric pdes singular liouville equation variational methods min-max schemes 35b33 53a30 53c21 81t13 |
| url | https://doi.org/10.1515/ans-2016-6013 |
| work_keys_str_mv | AT malchiodiandrea onsingularliouvilleequationsandsystems |