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Singular sets and the Lavrentiev phenomenon
Published online by Cambridge University Press: 28 September 2015
Abstract
We show that non-occurrence of the Lavrentiev phenomenon does not imply that the singular set is small. Precisely, given a compact Lebesgue null subset E ⊆ ℝ and an arbitrary superlinearity, there exists a smooth strictly convex Lagrangian with this superlinear growth such that all minimizers of the associated variational problem have singular set exactly E but still admit approximation in energy by smooth functions.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 3 , June 2015 , pp. 513 - 533
- Copyright
- Copyright © Royal Society of Edinburgh 2015
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