Timeline for variational characterization of the average of an $L^p$ function
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 26, 2013 at 12:22 | vote | accept | Josh | ||
| Apr 25, 2013 at 16:07 | vote | accept | Josh | ||
| Apr 25, 2013 at 16:10 | |||||
| Apr 25, 2013 at 14:00 | answer | added | ioannis.parissis | timeline score: 1 | |
| Apr 25, 2013 at 12:39 | history | edited | Josh | CC BY-SA 3.0 |
added 182 characters in body
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| Apr 25, 2013 at 10:59 | comment | added | Josh | I have not tried any example. I do not like to try for counterexamples. But if you have a counterexample you can answer, instead of commenting :-) | |
| Apr 25, 2013 at 10:49 | comment | added | Josh | That's why I wrote "I'm interested in the case $p \neq 2$". I expect something different when $p \neq 2$ (when computing the Euler-Lagrange equations), but still I have some motivation to believe that the result is still true for $p \neq 2$. | |
| Apr 25, 2013 at 6:37 | comment | added | Daniel Spector | Try taking the derivative of $f(c):=\int_\Omega |u-c|^p\;d\mu$, and then think about justifying it later (dominated convergence, etc). Then you can see why $c$ should be the average of $u$ when $p=2$, and what you might expect otherwise. | |
| Apr 25, 2013 at 0:12 | comment | added | Anthony Quas | Have you tried any examples? | |
| Apr 24, 2013 at 23:40 | history | asked | Josh | CC BY-SA 3.0 |