Timeline for Sobolev estimates $\|\nabla\phi\|_{\infty}\leq C\|\phi\|_{H^2}$
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2022 at 13:54 | comment | added | Mainak | Leoni's book has been a great resource, I was looking for an intro to Bounded variation spaces and distributions(the things Evans lack :P), this is great intro material. | |
| Jun 24, 2022 at 15:39 | comment | added | Willie Wong | The bound holds for $H^p$ functions with any $p > 1 + d/2$, where $d$ is the dimension. | |
| Jun 24, 2022 at 6:14 | comment | added | Mainak | Actually, what I needed was $\|\nabla\phi\|_{\infty}\leq C\|\phi\|_{H^p}$ for any p. It would be nice if it could be bounded in $H^2$. Any way thank you @WillieWong | |
| Jun 24, 2022 at 6:08 | vote | accept | Mainak | ||
| Jun 23, 2022 at 19:11 | review | Close votes | |||
| Jul 8, 2022 at 3:08 | |||||
| Jun 23, 2022 at 18:55 | comment | added | Michael Renardy | In two dimensions, the answer is also negative. Since this kind of result is easy to find in the literature, I am voting to close. | |
| Jun 23, 2022 at 17:33 | comment | added | Willie Wong | See my answer below. For a general resource on Sobolev spaces, see G Leoni's book published in the AMS graduate text series. | |
| Jun 23, 2022 at 17:32 | answer | added | Willie Wong | timeline score: 1 | |
| Jun 23, 2022 at 7:27 | comment | added | Mainak | I am not familiar with that, can you please elaborate or point me to a resource? | |
| Jun 21, 2022 at 15:25 | comment | added | Willie Wong | In dimension 3 or higher the inequality is false using a standard scaling argument. | |
| Jun 21, 2022 at 7:41 | history | edited | Glorfindel | CC BY-SA 4.0 |
added 1 character in body
|
| S Jun 21, 2022 at 7:38 | review | First questions | |||
| Jun 21, 2022 at 7:41 | |||||
| S Jun 21, 2022 at 7:38 | history | asked | Mainak | CC BY-SA 4.0 |