Timeline for Gagliardo-Nirenberg inequality
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 21, 2012 at 10:04 | comment | added | Welfar | Well, thank you for your answers Deane, that was very helpful! Actually I already known the easy proof for the basic inequality, I just didn't know too much about the interpolation one. | |
| Aug 21, 2012 at 9:59 | vote | accept | Welfar | ||
| Aug 20, 2012 at 14:33 | comment | added | Deane Yang | And you can figure out the value of $a$ by demanding that both sides of the inequality scale the same under rescaling the co-ordinate variable $x$ by a constant factor. This can also be said by assuming that $x$ has units (or, as you say, a "currency") associated to it and demanding that the induced units (which are powers of the units for $x$) corresponding to the two sides of the inequality must agree. | |
| Aug 20, 2012 at 14:21 | comment | added | Deane Yang | But you should also explain how the first inequality is proved using only the 1-dimensional fundamental theorem of calculus. And how the general inequality is proved using induction, integration by parts, and the Holder inequality. This is one of the easiest proofs of a deep fact that I've ever seen. I learned it from Nirenberg himself in a class he taught on PDE's. I can still remember it quite clearly, because it was so mind-boggling to me how easy it was. | |
| Aug 20, 2012 at 13:33 | history | answered | Bazin | CC BY-SA 3.0 |