Timeline for question on the proof of density of $C^{\infty}(M,N)$ in the sobolev space $W^{1,m}(M,N)$
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 9, 2011 at 13:41 | vote | accept | Italo | ||
| Jan 7, 2011 at 16:40 | answer | added | Deane Yang | timeline score: 1 | |
| Jan 7, 2011 at 16:13 | comment | added | Italo | it is correct $F_{\epsilon}(x)$ because $dist(F_{\epsilon}(x),N)\leq |F(y)-F_{\epsilon}(x)|$ for all $y\in B(x,\epsilon)$ so i should use that kind of estimate proceed | |
| Jan 7, 2011 at 16:05 | comment | added | Deane Yang | On the left, is the "$F_\epsilon(x)$" correct or should it be $F_\epsilon(y)$? | |
| Jan 7, 2011 at 15:59 | comment | added | Italo | I'm really sorry i made a copy and paste error, now i fixed it | |
| Jan 7, 2011 at 15:58 | history | edited | Italo | CC BY-SA 2.5 |
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| Jan 7, 2011 at 15:43 | comment | added | Denis Serre | The inequality is false twice. First, it is not homogeneous in $\epsilon$. The fraction is the right-hand side should be deleted. Now the second integral must be taken on a larger ball $B(x;2\epsilon)$, assuming that the support of $\phi_\epsilon$ is $B(x;\epsilon)$. | |
| Jan 7, 2011 at 15:41 | comment | added | Deane Yang | And have you tried to prove this inequality directly yourself using the fundamental theorem of calculus and the definition of $F_\epsilon$? What goes wrong? | |
| Jan 7, 2011 at 15:40 | comment | added | Deane Yang | I agree that the inequality does not look right. The two sides do not scale the same, do they? Are you supposed to have the $1/\mu(B(x,\epsilon))$ factor on both sides or just on the right? | |
| Jan 7, 2011 at 15:38 | history | edited | Denis Serre | CC BY-SA 2.5 |
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| Jan 7, 2011 at 15:31 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
TeX corrected
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| Jan 7, 2011 at 15:26 | history | edited | Denis Serre | CC BY-SA 2.5 |
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| Jan 7, 2011 at 15:18 | history | asked | Italo | CC BY-SA 2.5 |