Timeline for Extremal functions for Gagliardo-Nirenberg inequality
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2020 at 21:30 | vote | accept | user72012 | ||
| Jun 28, 2015 at 18:44 | comment | added | Deane Yang | For $\mathbb{R}^n$ or any other noncompact Riemannian manifold, I'm not sure. It's basically a question of showing that an appropriately normalized minimizing sequence of functions is compact with respect to some topology and that the limit is nonzero. The main issue here is making sure that the "mass" of the function does not leak out to infinity. If the domain is a closed Riemannian manifold, then the answer is yes. | |
| Jun 28, 2015 at 2:46 | comment | added | user72012 | Thanks very much, Deane. In the papers you gave, the authors can calculate the best constant GN(N,p,q,r) and extremal functions explicitly, of course for 1--parameter family of inequalities. So just assume that we don't care what the value of GN(N,p,q,r) is, but just the question that if GN(N,p,q,r) can be attained, can we show it in general? | |
| Jun 27, 2015 at 20:34 | history | edited | Deane Yang | CC BY-SA 3.0 |
added 469 characters in body
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| Jun 27, 2015 at 4:12 | history | answered | Deane Yang | CC BY-SA 3.0 |