Timeline for Operator on a Sobolev space
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 7, 2015 at 19:07 | comment | added | Joonas Ilmavirta | @user75795, yes, it means that they are the same element of $H^{-1}$. That means that they are the same when integrated against any function in $H^1_0$, which is the same as the usual weak definition. | |
| Jul 7, 2015 at 18:53 | comment | added | user75795 | So when i write $Lu=f$ with $ f \in L^2$ what does it mean? It means that they are the same operator, so they are the same element of $H^{-1}$? | |
| Jul 7, 2015 at 18:18 | history | edited | Joonas Ilmavirta | CC BY-SA 3.0 |
added 332 characters in body
|
| Jul 7, 2015 at 16:44 | comment | added | Joonas Ilmavirta | @user75795, yes, that is the same thing. You can define $L$ using $B$ in this way. But you should check that it agrees with the classical definition for smooth functions. (I removed my earlier comment, which was a respond to an earlier version of your comment.) | |
| Jul 7, 2015 at 16:40 | comment | added | user75795 | Thanks. Isn't this the bilinear form $B[u,v]$ associated with $L$? So what's the difference between $L$ and $B[u,v]$? $$ \langle Lu,v\rangle = \int_\Omega -a_{ij}D_juD_iv+b_iD_iuv+cuv. $$ | |
| Jul 7, 2015 at 16:30 | history | answered | Joonas Ilmavirta | CC BY-SA 3.0 |