Universal singular sets for one-dimensional variational problems

J. M. Ball, N. S. Nadirashvili

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)429-438
Number of pages10
JournalCalculus of Variations and Partial Differential Equations
Issue number4
Publication statusPublished - Oct 1993


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