### Abstract

A study is made of the regularity properties of minimizers u of the integral I(u)=?_{a}^{b}f(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.

Original language | English |
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Pages (from-to) | 429-438 |

Number of pages | 10 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 1 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 1993 |

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## Cite this

Ball, J. M., & Nadirashvili, N. S. (1993). Universal singular sets for one-dimensional variational problems.

*Calculus of Variations and Partial Differential Equations*,*1*(4), 429-438. https://doi.org/10.1007/BF01206961