Timeline for Notation for weak derivatives
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 3 at 10:16 | comment | added | terceira | The decisive difference is between the classical derivative of a $C^1$-function and the distributional derivative of anything else that can be regarded as a distribtion (measure, locally integrable function, rational function $\dots$). In his elementary treatment, Sebastião e Silva used $D$ for the first, $\tilde D$ for the latter. This can be extended to the multivariate case, and higher derivatives, by using Schwartz' superscript notation. | |
| May 3 at 8:26 | vote | accept | Alessandro Della Corte | ||
| May 3 at 8:17 | answer | added | Ayman Moussa | timeline score: 5 | |
| May 2 at 19:17 | comment | added | Alessandro Della Corte | @PietroMajer well, not so sure. By $\sum$ you still mean a sum. You may ask for different notations for the symbol indicating the kind of convergence. And indeed you have at least some: $\to$, $\rightharpoonup$, the same with * above, etc... | |
| May 2 at 19:09 | comment | added | Pietro Majer | I'd would not recommend different notations. The situation is similar to the series notation $\sum_{k=0}^\infty f_k$: in what sense does it converge? If needed, one may say it in parentheses. | |
| May 2 at 16:22 | comment | added | Alessandro Della Corte | @WillieWong Yeah, indeed: even authors who are very careful distinguishing elements of Lebesgue/Sobolev spaces from functions as a rule use the same notation for classical and weak diff. operators. | |
| May 2 at 16:16 | comment | added | Willie Wong | My guess is that you need to look for those notes which emphasize the fact that weak derivatives are only unique at the equivalence class level, and not on the function level; though Evans and Gariepy (which often distinguishes between a Sobolev function and its equivalence class) doesn't seem to use a separate notation for weak differentiation. | |
| May 2 at 16:13 | comment | added | Willie Wong | I wouldn't say it is "established", but Joa Weber's lecture notes uses the $\partial$ and $D$ operators for the classical derivatives, and the subscript notation $u_{x_i}$ for weak derivatives. // I also remember seeing once some lecture notes using ${}^{(w)}\partial$ for weak differentiation, but that was a while ago and I don't remember whom by. | |
| May 2 at 15:33 | history | edited | Alessandro Della Corte | CC BY-SA 4.0 |
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| May 2 at 15:28 | history | asked | Alessandro Della Corte | CC BY-SA 4.0 |