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EnglishMotivated by the study of gauge field vortices we consider a mean field equation on the standard two-sphere involving a Dirac distribution supported at a point P of S^2. As needed for the applications, we show that solutions ”concentrate” exactly at P for some limiting value of a given parameter. We use this fact to obtain symmetry (about the axis OP) and uniqueness property for the solution. The presence of the Dirac measure makes such a task particularly delicate. Indeed, we need to rule out the possibility that, after blow up (in a suitable scale), the solution sequence may admit a double ”peak” profile described in terms of appropriate “limiting” problems. For instance we need to account for the presence of non-axially symmetric solutions in such ”limiting” problems. In this process, we establish a symmetry result about a maximal circle through P and its antipodal point P*, that applies to more general situations where the full axial symmetry cannot be expected.
Bartolucci, D., Lin, C., & Tarantello, G. (2011). Uniqueness and symmetry results for solutions of a mean field equation on S^2 via a new bubbling phenomenon. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 64(12), 1677-1730.
| Tipologia: | Articolo su rivista |
| Citazione: | Bartolucci, D., Lin, C., & Tarantello, G. (2011). Uniqueness and symmetry results for solutions of a mean field equation on S^2 via a new bubbling phenomenon. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 64(12), 1677-1730. |
| Altre informazioni significative: | project FIRB-Ideas Analysis and Beyond; MiUR project Variational methods and nonlinear PDEs |
| IF: | Con Impact Factor ISI |
| Lingua: | English |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
| Revisione (peer review): | Esperti anonimi |
| Tipo: | Articolo |
| Rilevanza: | Rilevanza internazionale |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1002/cpa.20385 |
| Stato di pubblicazione: | Pubblicato |
| Data di pubblicazione: | dic-2011 |
| Titolo: | Uniqueness and symmetry results for solutions of a mean field equation on S^2 via a new bubbling phenomenon |
| Autori: | |
| Autori: | Bartolucci, D; Lin, C; Tarantello, G |
| Appare nelle tipologie: | 01 - Articolo su rivista |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| BLT-CPAM-Vol64-issue(12)-December(2011).pdf | Articolo principale | N/A | Copyright dell'editore | Administrator Richiedi una copia |
http://hdl.handle.net/2108/13623
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