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Mar 1, 2018 at 13:57 comment added Rym Touibi Hence, for every $t\in (0,T)$, we get $x\mapsto f(x,t) \in L^{2}(D) ,$ what I need.
Mar 1, 2018 at 13:31 comment added Rym Touibi It means that: $||f(.,t)||_{L^{2}(D)}\leq k ||f||_{H^{1}(D)}$ with $K$ is a constant
Mar 1, 2018 at 12:21 comment added Jochen Wengenroth What do you mean by "the continuous embedding"? Shouldn't it be a well-defined version of $f \mapsto f(\cdot,t)$? This is never injective and hence, I would not call this an embedding.
Mar 1, 2018 at 12:00 history edited Rym Touibi CC BY-SA 3.0
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Feb 28, 2018 at 16:56 history asked Rym Touibi CC BY-SA 3.0