Timeline for Density of certain functions in $C_c^\infty(0,T;V)$ in the space $W(0,T) \approx H^1(0,T;V)$?
Current License: CC BY-SA 3.0
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| Jul 18, 2013 at 21:07 | comment | added | aere | Ah, I see. I will edit my post then. Thanks for pointing it out. | |
| Jul 18, 2013 at 19:11 | comment | added | Michael Renardy | Lions and Magenes use the notation ${\cal D}([a,b])$ to denote $C^\infty$ functions with compact support in the closed interval $[a,b]$. The condition of compact support is of course redundant in this case unless the interval is infinite. This should not be confused with ${\cal D}(a,b)$, which is a set of functions which have support which is compact in the open interval $(a,b)$. | |
| Jul 18, 2013 at 18:16 | comment | added | aere | Thanks for replying. But is not $C_c^\infty(0,T;V) = \mathcal{D}(0,T;V)$? The latter (defined as infinitely differentiable compactly-supported $V-$valued functions) is dense in $W(0,T)$ by a theorem of Lions and Magenes. | |
| Jul 18, 2013 at 18:12 | history | answered | Michael Renardy | CC BY-SA 3.0 |