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Oct 3, 2020 at 2:54 comment added Michael Renardy (B) is the correct definition, in particular, there is no requirement (or theorem) that $u'\in L^1(0,T,H^1_0)$. The "little miracle" comes from the smoothness of $\varphi$ which makes the integration by parts possible.
Oct 3, 2020 at 0:19 history edited Yuval CC BY-SA 4.0
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Oct 2, 2020 at 23:27
Oct 2, 2020 at 21:11 history asked Yuval CC BY-SA 4.0