In this report, we demonstrate the existence of variational problems with infima that depend continuously upon the Sobolev space from which the competing functions are taken. It is shown, for each in a particular class of continuous functions, that there is a variational integral and boundary conditions such that, for every , the infimum is equal to if the admissible class is a subset of W^1,p. So the manner in which the infimum depends upon the Sobolev exponent may be prescribed.