I have a question about AubinLions Lemma, the standard AubinLions lemma need those Banach Space be reflexive spaces, are there any version of AubinLions without reflexivity?
Standard aubinlions:http://en.wikipedia.org/wiki/AubinLions_lemma
I have a question about AubinLions Lemma, the standard AubinLions lemma need those Banach Space be reflexive spaces, are there any version of AubinLions without reflexivity? Standard aubinlions:http://en.wikipedia.org/wiki/AubinLions_lemma 


I was wondering the same recently, and it seems to my that the answer is yes (you can get rid of reflexivity). Look at the paper of Jacques Simon : Compact sets in the spaces $L^p(0,T,B)$. The paper claims to give sharp results in any regard and as far as I can see it only asks the spaces to be banach he gives for example Corollary 4 : if $\{F\}$ is bounded in $L^q(0,T,X), \{F^\prime\}$ bounded in $ L^1(0,T,Y),$ with the usual assumption :$$X\underset{compact}{\hookrightarrow} B\underset{continous}{\hookrightarrow}Y,$$ then $\{F\}$ is relatively compact in $L^p(0,T,B)$, for $p<q$ where $X,B,Y$ are only Banach (assumption 8.1 in the paper). The corresponding result holds for $\{F\}\subset L^\infty$ and $\{F^\prime\}\subset L^r$ with $r>1$ (gives relative compactness in $\mathcal{C}(0,T,B)$). I guess this is why it is sometimes mentionned as AubinLionsSimon's lemma ... 

