UNIVERSAL SINGULAR SETS FOR ONE-DIMENSIONAL VARIATIONAL-PROBLEMS

A study is made of the regularity properties of minimizers u of the integral I(u) = integral-b/a f(x, u, u') dx subject to the boundary conditions u(a) = alpha, u(b) = beta as the interval (a, b) and boundary values alpha,beta 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.