In my assignment I have a Leontief (perfect complements) function u(x,y)=min(x,2y). Keeping utility fixed, we minimize the expenditure. Since we have a Leontief function, at a fixed level of utility u(x,y)=u expenditure is minimized at the angle point, where x=2y. Since utility is fixed at u=min(x,2y), hence u=min(2y,2y)=2y and u=2y=x. Therefore Hicksian demands will be x=u and y=u/2.
The next part of my assignment is to prove that compensated demand function is homogeneous of degree 0 in prices both for this case and in general. However, in my case (as well as for the standard Leontief function) compensated demand function does not depend on prices. It is unlikely that I derived the wrong functions, since for the standard Leontief function compensated demand also does not depend on the prices.