Timeline for Looking for higher order Sobolev inequality
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 7, 2013 at 20:28 | comment | added | Chris | @Deane thank you so much. I better do some more learning! | |
| Jan 7, 2013 at 20:24 | comment | added | Deane Yang | Chris, any domain with smooth boundary satisfies the cone condition. You would cover the manifold by open sets that are diffeomorphic to a ball and apply the result in Adams to the function multiplied by the appropriate cutoff function restricted to one of the open sets and pulled back to the ball. | |
| Jan 7, 2013 at 20:20 | comment | added | Chris | Thanks, I'll read up on Ehrling's lemma. @Deane But Adams requires the domain to satisfy a cone condition, which I want to avoid. | |
| Jan 7, 2013 at 20:05 | comment | added | Deane Yang | But if you mean to use the $H^2$ norm on the RHS, then this is indeed an interpolation inequality. It indeed is probably in Adams for function on a domain in $R^n$, but this can be transferred to a manifold using co-ordinate charts and a partition of unity. | |
| Jan 7, 2013 at 20:03 | comment | added | Michael Renardy | If you put the $H^2$ norm on the right hand side instead of the $H^1$ norm, this is Ehrling's lemma, which is well known. | |
| Jan 7, 2013 at 20:00 | comment | added | Deane Yang | If $\|u\|_{H^1} = \|\nabla u\|_{L^2} + \|u\|_{L^2}$, I don't see how this could be true. | |
| Jan 7, 2013 at 19:38 | comment | added | Chris | @timur: but I find that most such questions on MSE go unanswered so thought this would be a better place. Also I don't think this question is "common knowledge" so to speak. | |
| Jan 7, 2013 at 19:37 | history | edited | Chris | CC BY-SA 3.0 |
added 6 characters in body
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| Jan 7, 2013 at 19:20 | comment | added | timur | If I understood correctly, what you are looking for is interpolation inequalities. The question is more suitable for MSE. | |
| Jan 7, 2013 at 12:54 | history | asked | Chris | CC BY-SA 3.0 |