Timeline for Compact embeddings of Sobolev spaces: a counterexample showing the Rellich-Kondrachov theorem is sharp
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2021 at 9:37 | comment | added | Pietro Majer | Actually no comment | |
| Apr 7, 2021 at 23:11 | comment | added | Yemon Choi | Apologies for coming back to very old material, but do you have any comment on the the answers below which claim that there is something amiss in your answer? | |
| Nov 4, 2015 at 14:53 | comment | added | tomglabst | You can find this in Adams, Sobolev Spaces. | |
| Jan 7, 2015 at 15:32 | comment | added | Pietro Majer | @QA Ngô In fact, $u_\epsilon\to0$ a.e., in $L^{p^*}$, and in $W^{1,p}$, as $\epsilon\to0$. The claim is on the normalized family: check the last lines. | |
| Jan 7, 2015 at 12:56 | comment | added | QA Ngô | In this answer, it is not clear to see why the sequence $\{u_\varepsilon\}_\varepsilon$ has no convergent subsequence in $L^{p^\star}$. Basically, there are two types of lacking the compactness property: Unbounded domains and critical exponents. In both cases, it is more convenient to dilate a "good" function plus a scaling of this function if working in bounded domains. | |
| Sep 5, 2013 at 17:16 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Nov 16, 2011 at 16:16 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Nov 16, 2011 at 10:15 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Nov 16, 2011 at 7:24 | history | answered | Pietro Majer | CC BY-SA 3.0 |