Where can I find a proof that $\mathcal{D}(0,T;V)$ (the space of $V$-valued compactly supported functions on $[0,T]$) is dense in the space $W(0,T)$, where $$W(0,T) := \{ u \in L^2(0,T;V) : u' \in L^2(0,T;V^*)\},$$ where $V$ is Hilbert\Banach? I need the proof in the English language.
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$\begingroup$ What is $T$? What do the $0$s mean? What is $\mathcal{D}$? Is this question research-level? $\endgroup$– Benoît KloecknerCommented May 10, 2013 at 16:55
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$\begingroup$ $[0,T]$ is an interval. This is a research-level question. $\endgroup$– maximumtagCommented May 10, 2013 at 17:11
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2$\begingroup$ A standard reference on this is the monograph by Lions and Magenes: Non-Homogeneous Boundary Value Problems and Applications. Everyone refers to it for the proof... $\endgroup$– András BátkaiCommented May 10, 2013 at 17:55
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1$\begingroup$ Volume 1: rd.springer.com/book/10.1007/978-3-642-65161-8/page/1 , but there are three. $\endgroup$– András BátkaiCommented May 10, 2013 at 17:57
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$\begingroup$ @AndrasBatkai thank you a lot. Unfortunately I don't have access to that. Do you have a PDF of that (if legal, otherwise obviously ignore this)? $\endgroup$– maximumtagCommented May 10, 2013 at 21:04
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