Timeline for Concentration compactness. Can this concept be stated in a theorem?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2017 at 12:11 | vote | accept | Zinkin | ||
| Aug 26, 2017 at 8:17 | comment | added | Denis Serre | Deane, I am on the same tune as you. | |
| Aug 25, 2017 at 22:41 | comment | added | Deane Yang | Denis, you're right. Concentrated compactness usually appears when the loss of compactness is due to an invariance under a noncompact group action, whether it be rescaling or translations. When it's rescaling, then the loss of compactness causes the energy functional to be critical, and it's studied using blow up arguments. When it's translation invariance, the energy functional does not have to be critical. | |
| Aug 25, 2017 at 20:43 | comment | added | Denis Serre | The criticality of the energy is actually not an issue. In practice, the lack of compactness is due to the translation invariance of the problem at hand. For instance, P.-L. Lions and I. Catto have proved, using CC, the existence of a ground state for neutral systems of elementary particles, in the Hartree and Thomas-Fermi models. | |
| Aug 25, 2017 at 19:48 | history | answered | Deane Yang | CC BY-SA 3.0 |