Universal singular sets for one-dimensional variational problems

J. M. Ball; N. S. Nadirashvili

doi:10.1007/BF01206961

Universal singular sets for one-dimensional variational problems

J. M. Ball, N. S. Nadirashvili

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

A study is made of the regularity properties of minimizers u of the integral I(u)=?_a^bf(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
Pages (from-to)	429-438
Number of pages	10
Journal	Calculus of Variations and Partial Differential Equations
Volume	1
Issue number	4
DOIs	https://doi.org/10.1007/BF01206961
Publication status	Published - Oct 1993

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title = "Universal singular sets for one-dimensional variational problems",

abstract = "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. {\textcopyright} 1993 Springer-Verlag.",

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AB - 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.

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DO - 10.1007/BF01206961

M3 - Article

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

ER -

Universal singular sets for one-dimensional variational problems

Abstract

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