A study is made of the regularity properties of minimizers u of the integral I(u)=?abf(x, u, u') dx subject to the boundary conditions u(a)=a, u(b)=ß as the interval (a, b) and boundary values a,ß 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. © 1993 Springer-Verlag.
|Number of pages||10|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - Oct 1993|