Timeline for how to use the sobolev inequality to obtain the embedding theorem
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 11, 2017 at 12:49 | history | bounty ended | CommunityBot | ||
| Apr 11, 2017 at 4:16 | vote | accept | pxchg1200 | ||
| Apr 10, 2017 at 12:23 | comment | added | Henry.L | intlpress.com/site/pub/files/_fulltext/journals/cag/1994/0002/… Yes you are right, correct the cite. I do not understand what you commented above, but it seems to me that [2] is an more precise version. Let me know why [2] cannot lead to [1]. @pxchg1200 | |
| Apr 10, 2017 at 12:16 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Apr 10, 2017 at 2:17 | comment | added | pxchg1200 | I can't find Theorem 1.2 in [2], I think your reference of [2] should be [2] Capogna L, Danielli D, Garofalo N. The geometric Sobolev embedding for vector fields and the isoperimetric inequality[J]. Comm. Anal. Geom, 1994, 2(2): 203-215. I am very appreciate for your answer, however, By the partition of unity, it seems we can only obtain $$\|f\|_{L^{q}(U)}\leq C( \|D_{L}f\|_{L^{p}(U)}+\|f\|_{L^{p}(U)} )$$ for $f\in S_{0}^{1,p}(U)$. it seems we need a poincare inequality to obtain $$\|f\|_{L^{q}(U)}\leq C( \|D_{L}f\|_{L^{p}(U)}) $$ for $f\in S_{0}^{1,p}(U)$ | |
| Apr 8, 2017 at 18:00 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Apr 8, 2017 at 14:09 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Apr 8, 2017 at 14:03 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Apr 8, 2017 at 13:52 | history | answered | Henry.L | CC BY-SA 3.0 |