Summary. A study is made of the regularity properties of minimizers u of the integral x, u, u ) dx subject to the boundary conditions u(a) = o~, u(b) = r as the interval (a, b) and boundary values o~,/3 are varied. Under natural hypotheses on f it is shown that the set of points in the (x, u)-plane at which a minimizer u can have infinite derivative for some interval and boundary values is small in the sense of category
