Timeline for Condition to obtain a not compact embedding
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 2, 2019 at 9:33 | vote | accept | Vrouvrou | ||
| Oct 8, 2015 at 6:56 | history | edited | Jean Van Schaftingen | CC BY-SA 3.0 |
Corrected typo
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| Jun 9, 2015 at 20:49 | comment | added | Vrouvrou | please explain me how you find that $v_{\lambda}$ do not converge to 0 in $L^{p^*}_{\alpha}$ | |
| Jun 9, 2015 at 20:26 | comment | added | Vrouvrou | also we have that $||v_{\lambda}||_{L^{p^*}_{\alpha}}=||v||_{L^{p^*}_{\alpha}}$ if and only if $\alpha =0$ impossible ! | |
| Jun 9, 2015 at 20:14 | comment | added | Vrouvrou | but why it is bounded please, why convergence almost every where imply the weak convergence > | |
| Jun 9, 2015 at 20:08 | comment | added | Jean Van Schaftingen | The week convergence comes from the fact that the sequence is bounded in norm and converges almost everywhere as $\lambda \to 0$. | |
| Jun 9, 2015 at 19:20 | comment | added | Vrouvrou | Please give me an answer how we prove the weak convergence ? | |
| Jun 8, 2015 at 6:56 | comment | added | Vrouvrou | I think that we have this when $\lambda$ goes to $+\infty$ not near $0$ look at $1-\frac{N}{p}$ it is negative | |
| Jun 6, 2015 at 17:29 | comment | added | Vrouvrou | I proved that there is a compact injection between $W^{1,p}_0$ and $C_{\theta}=\{u\in C(\overline{\Omega}), \sup (|x|^{\theta} |u(x)|)<\infty\}$ for $\theta>\frac{N}{p}$ and there is a continuous injection between $C_{\theta}$ and $L^{p^*}_{\theta}$ so where is the contradiction ? | |
| Jun 4, 2015 at 7:19 | comment | added | Jean Van Schaftingen | It converges almost everywhere to (0) as (\lambda \to 0), whereas its norm does not converge to (0). | |
| Jun 4, 2015 at 6:31 | comment | added | Vrouvrou | Can you give me more details why $(\varphi_{\lambda})$ is not relatively compact ? what about if we replace $p^*$ by any $q>p$ ? thank you | |
| Jun 1, 2015 at 8:52 | comment | added | Jean Van Schaftingen | Yes, that is it. | |
| May 29, 2015 at 7:24 | comment | added | Vrouvrou | This means that $W^{1,p}_0$ is not compactly embeded in any space $L^{p^*}_{\alpha}$ right ? | |
| May 28, 2015 at 8:36 | comment | added | Jean Van Schaftingen | There is no condition on $\alpha$. | |
| May 28, 2015 at 7:57 | comment | added | Vrouvrou | What i the condition on $\alpha$ ? thank you | |
| May 28, 2015 at 6:50 | history | answered | Jean Van Schaftingen | CC BY-SA 3.0 |