Singular sets and the Lavrentiev phenomenon

Richard Gratwick

doi:10.1017/S0308210513001510

Singular sets and the Lavrentiev phenomenon

Richard Gratwick

School of Mathematics

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

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 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.

Original language	English
Pages (from-to)	513-533
Number of pages	21
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	145
Issue number	3
DOIs	https://doi.org/10.1017/S0308210513001510
Publication status	Published - 28 Sept 2015

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Singular sets and the Lavrentiev phenomenon

Abstract

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