Timeline for What are the bounds of $xy^{y^a/x^a} + yx^{x^a/y^a} - x^a - y^a$ for $0 \le x \le 1$ and $a > 0$?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 1, 2023 at 4:38 | vote | accept | Nilotpal Kanti Sinha | ||
| May 9, 2023 at 18:36 | answer | added | Willie Wong | timeline score: 2 | |
| May 9, 2023 at 15:21 | comment | added | Willie Wong | actually: do you have numerical simulations for $a \in [3,10)$? My previous comment is wrong. When $a$ is large, it seems that the maximum may also be attained on the diagonal. | |
| May 9, 2023 at 14:28 | comment | added | Willie Wong | The upper bound when $a \geq 1$ is probably attained when one of $x,y$ tends to zero. If this is true than a computation would show $C_a = \left(\frac1a\right)^{\frac1{a-1}} - \left(\frac1a\right)^{\frac{a}{a-1}}$. | |
| May 9, 2023 at 14:21 | comment | added | Willie Wong | The lower bound when $a \leq 2$ is probably attained along the line $x = y$; if that is true than an elementary computation would give $c_a = 2\left[ \left( \frac2a\right)^{\frac2{a-2}} - \left( \frac2a \right)^{\frac{a}{a-2}} \right]$. | |
| May 9, 2023 at 13:30 | answer | added | Iosif Pinelis | timeline score: 4 | |
| May 9, 2023 at 5:37 | history | asked | Nilotpal Kanti Sinha | CC BY-SA 4.0 |