The Mean Field Equation with Critical Parameter in a Plane Domain
| dc.creator | Ni, Yilong | |
| dc.date | 2006-11-08 | |
| dc.date.accessioned | 2026-07-07T07:32:40Z | |
| dc.date.available | 2026-07-07T07:32:40Z | |
| dc.description | Consider the mean field equation with critical parameter $8π$ in a bounded smooth domain $Ω$. Denote by $E_{8π}(Ω)$ the infimum of the associated functional $I_{8π}(Ω)$. We call $E_{8π}(Ω)$ the "energy" of the domain $Ω$. We prove that if the area of $Ω$ is equal to $π$, then the energy of $Ω$ is always greater or equal to the energy of the unit disk and equality holds if and only if $Ω$ is the unit disk. We also give a sufficient condition for the existence of a minimizer for $I_{8π}(Ω)$. | |
| dc.description | 13 pages, to appear in Differential and Integral Equations | |
| dc.identifier | https://arxiv.org/abs/math/0611246 | |
| dc.identifier | http://arxiv.org/abs/math/0611246 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119189 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J60; 35J20; 49J10 | |
| dc.title | The Mean Field Equation with Critical Parameter in a Plane Domain | |
| dc.type | text |