%0 Journal Article
%T A one-dimensional variational problem with continuous Lagrangian and singular minimizer
%A Richard Gratwick
%A David Preiss
%J Mathematics
%D 2010
%I arXiv
%R 10.1007/s00205-011-0413-3
%X We construct a continuous Lagrangian, strictly convex and superlinear in the third variable, such that the associated variational problem has a Lipschitz minimizer which is non-differentiable on a dense set. More precisely, the upper and lower Dini derivatives of the minimizer differ by a constant on a dense (hence second category) set. In particular, we show that mere continuity is an insufficient smoothness assumption for Tonelli's partial regularity theorem.
%U http://arxiv.org/abs/1002.3070v2