There is a theorem in Evans partial differential equation book as follows:
if $u \in W^{1,p}(U)$ then for each compact $V$ in $U$ we have that: $ |D^hu|_{L^p(V)} \leq C |Du|_{L^p(U)} $ for all $ |h| < \frac{1}{2} dist(\partial U, V)$
now I have read the proof and its a simple theorem indeed but I have no idea why that factor 1/2 is given in theorem. It seems to me the same thing can be said for all $ |h| < dist(\partial U, V)$ Thanks
