Timeline for General version of Weyl's lemma
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2022 at 14:12 | comment | added | Giorgio Metafune | The argument is a variation of regularity results and I do not know any place where it is written in the form you ask for. However, if $p>1$, these arguments are explaind in Lemma 2.5 in uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.020/arendt/…. If you need $p=1$ Iet me know. | |
| Nov 12, 2022 at 9:58 | comment | added | W.J. | @Giorgio Metafune Thanks a lot! So can you recommend me some books or papers about this method that you said? I am a little confused about difference quotients methods and the problem of p. | |
| Nov 11, 2022 at 14:45 | comment | added | Giuseppe Di Fazio | Yes, for smooth coefficients your statement is true. | |
| Nov 10, 2022 at 17:54 | comment | added | Giorgio Metafune | For smooth coefficients the result is true. It follows by combining difference quotients methods and $W^{2,p}$ estimates if $u \in L^p_{loc}$ for some $p>1$. If $p=1$ one needs first an argument to show that it is in $L^p_{loc}$. | |
| Nov 10, 2022 at 14:49 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor Math Jaxing
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| Nov 10, 2022 at 13:17 | comment | added | W.J. | So when a_{i,j} is smooth, does the claim hold? In this case I think the regularity is not a problem, but I am still not sure whether the Weyl lemma holds. | |
| Nov 10, 2022 at 13:07 | history | answered | Giuseppe Di Fazio | CC BY-SA 4.0 |