Timeline for Intuition behind choosing a specific test function
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 27, 2020 at 6:09 | comment | added | Connor Mooney | @QuartoBendir: Thank you for the precise references for example (4) | |
| Aug 27, 2020 at 6:08 | comment | added | Connor Mooney | @YongminPark: my pleasure | |
| Aug 27, 2020 at 4:41 | comment | added | Quarto Bendir | The first place I'm aware of the log trick is in theorem 2 of Moser "A new proof of De Giorgi's theorem". Moser says that the proof was inspired by Bers & Nirenberg "On linear and non-linear elliptic boundary value problems in the plane", so possibly it appears there too | |
| Aug 27, 2020 at 4:26 | comment | added | Quarto Bendir | The estimate in #4 is due to Yau "Harmonic functions on complete Riemannian manifolds" and Cheng-Yau "Differential equations on Riemannian manifolds". Li-Yau are responsible for the parabolic analogue. By considering a harmonic function on the unit ball as a solution of a different elliptic equation on the ball model of hyperbolic space, and max principle for noncompact spaces, Yau showed that $|\nabla\log u|^2\leq \frac{c(n)}{1-|x|^2}$ if $\inf u=0$. Cheng-Yau got the version you state by using cutoff functions and the usual max principle. | |
| Aug 27, 2020 at 3:24 | comment | added | Yongmin Park | Thanks very much! Now I have better understading about the proof. Thank you for the other examples, too. | |
| Aug 27, 2020 at 3:02 | vote | accept | Yongmin Park | ||
| Aug 27, 2020 at 3:01 | vote | accept | Yongmin Park | ||
| Aug 27, 2020 at 3:02 | |||||
| Aug 27, 2020 at 3:01 | vote | accept | Yongmin Park | ||
| Aug 27, 2020 at 3:01 | |||||
| Aug 27, 2020 at 2:18 | history | edited | Connor Mooney | CC BY-SA 4.0 |
added 5 characters in body
|
| Aug 27, 2020 at 0:41 | history | edited | Connor Mooney | CC BY-SA 4.0 |
added 207 characters in body
|
| Aug 26, 2020 at 22:17 | history | edited | Connor Mooney | CC BY-SA 4.0 |
added 277 characters in body
|
| Aug 26, 2020 at 21:20 | history | edited | Connor Mooney | CC BY-SA 4.0 |
added 61 characters in body
|
| Aug 26, 2020 at 20:34 | history | edited | Connor Mooney | CC BY-SA 4.0 |
added 11 characters in body
|
| Aug 26, 2020 at 20:16 | history | edited | Connor Mooney | CC BY-SA 4.0 |
added 32 characters in body
|
| Aug 26, 2020 at 19:36 | history | edited | Connor Mooney | CC BY-SA 4.0 |
added 16 characters in body
|
| Aug 26, 2020 at 18:09 | history | edited | Connor Mooney | CC BY-SA 4.0 |
added 5 characters in body
|
| Aug 26, 2020 at 17:51 | history | edited | Connor Mooney | CC BY-SA 4.0 |
added 15 characters in body
|
| Aug 26, 2020 at 17:45 | history | answered | Connor Mooney | CC BY-SA 4.0 |