Timeline for Are there $f, g$ such that $\int_{S^{1}} |f'|^{2}+|g'|^{2}d\theta-2\int_{S^{1}}f'g<0,$ where $f'=\frac{\partial f}{\partial \theta}$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2020 at 4:53 | vote | accept | liding | ||
| Jul 31, 2020 at 18:20 | comment | added | Giorgio Metafune | Of course, yes. Take $f(t)=-\cos t, g(t)=\sin t$, then you get equality with $C=2$. | |
| Jul 31, 2020 at 17:03 | comment | added | liding | Thank you! For general constant $C$, are there functions $f,g$ such that $$\int_{S^{1}} |f'|^{2}+|g'|^{2}d\theta-C\int_{S^{1}}f'g<0$$? | |
| Jul 31, 2020 at 9:43 | history | answered | Giorgio Metafune | CC BY-SA 4.0 |