Timeline for Optimal $L_p$-estimate for elliptic operator
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2016 at 15:47 | comment | added | Student | In fact it is not solved, so I asked for reference, but now I think this can be hard done, and it was also mentioned in Grisvard's book "elliptic problems in non smooth domains" that the inverse norm is very non optimal for $p>2$. For the case $p=2$, an optimal estimate can be obtained by using Mikhlin's theorem and Plancherel's equality, so was mentioned by his book, but i can not find the source anymore. | |
| Dec 15, 2016 at 14:39 | comment | added | Giuseppe Di Fazio | Could you give a reference of the paper in which the problem has been solved for the operator \Delta? | |
| Dec 15, 2016 at 9:47 | comment | added | Student | Yes, I think the problem I have is that I may need an optimal estimate for the inverse operator norm, which is $c$ in your work, for some kind of fixed point theorem, but I think the optimality is not given in your work. And also, I think it is very hard to give an optimal estimate for the case $p>2$, since we need many estimates in between and this makes it difficult. Maybe I should find another way to do this problem. | |
| Dec 14, 2016 at 21:30 | comment | added | Giuseppe Di Fazio | Iif you are still in trouble feel free to ask | |
| Dec 14, 2016 at 14:36 | history | answered | Giuseppe Di Fazio | CC BY-SA 3.0 |