Timeline for Sobolev inequality on the sphere derivation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2021 at 23:42 | comment | added | Deane Yang | One difficulty is computing the gradient of a function $f$ on the sphere. My suggestion is to extend the function to a function $\tilde{f}: \mathbb{R}^n\backslash\{0\} \rightarrow \mathbb{R}$ homogeneous of degree $0$. In other words, let $$ \tilde{f}(x) = f\left(\frac{x}{|x|}\right). $$ Then the gradient of $\tilde{f}$ is equal to the spherical gradient of $f$, because $x\cdot \nabla \tilde{f} = 0$. | |
| Nov 28, 2021 at 12:44 | history | edited | Student | CC BY-SA 4.0 |
added 787 characters in body
|
| S Nov 18, 2021 at 16:00 | history | suggested | CommunityBot | CC BY-SA 4.0 |
use of \tag{} in MathJax
|
| Nov 17, 2021 at 0:51 | review | Suggested edits | |||
| S Nov 18, 2021 at 16:00 | |||||
| Nov 15, 2021 at 16:12 | comment | added | Student | @GiuseppeNegro thanks for sharing this reference! | |
| Nov 15, 2021 at 16:07 | comment | added | Giuseppe Negro | This is explained in detail in the book "Analysis" of Lieb and Loss, section 4.4. | |
| Nov 15, 2021 at 15:11 | history | asked | Student | CC BY-SA 4.0 |