I am studying asymptotic analysis of periodic medium. Epsi is the periodic parameter. aij are considered regular. Here I have $$a_{ij} ^\epsilon (x) = a_{ij} (\frac{x} {\epsilon}) $$ And it says that this function would has derivative of order $\frac{1} {\epsilon} $. I think its like $x^3 $ has derivative of order three. But if I consider $\frac{x} {4} $ it's seems wrong.
Also when we talk about x belongs bounded subset of $R^n *] 0,T[$ This model turns into $$ a_{ij} ^\epsilon (x, t) = a_ij ( x, \frac{x} {\epsilon} , t, \frac{t} {\epsilon^k)$$
And then says it not have bounded derivative with respect to t. (https://i.stack.imgur.com/uKVLW.jpg) I want a clear idea so I can move further with clear concepts.
