Timeline for Compact embeddings of Sobolev spaces: a counterexample showing the Rellich-Kondrachov theorem is sharp
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 16, 2020 at 15:17 | comment | added | user165965 | In respect of the Question raised by Ànonimous',if only one can,and indeed one should inevitably,give-up using the àpriori given,generic'Lebesgue norm and use instead the gradient estimated(from a reproducing kernel formula) Lebesgue norm,the dilemma is resolved for good.Indeed by a well known finite measure theoretic result of A.Villani,Rellich-Kondrachov compactness(RK) seen for q<p* is transferred to RK at p* by Cauchy Continuity.Thus any measure of non-compactness at p* has to be zero.The inf.metric on W^(1,p) on the bounded set is incomplete as well in respect of a uniform gauge. | |
| Jul 30, 2020 at 10:56 | history | edited | Pietro Majer | CC BY-SA 4.0 |
added 17 characters in body
|
| Sep 29, 2015 at 19:18 | review | Late answers | |||
| Sep 29, 2015 at 22:36 | |||||
| Jul 23, 2013 at 11:33 | review | Suggested edits | |||
| Jul 23, 2013 at 11:38 | |||||
| Jul 11, 2012 at 1:59 | history | answered | Nagaraj | CC BY-SA 3.0 |