Singular Sets and the Lavrentiev Phenomenon
Classical Analysis and ODEs
2019-07-22 v1
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 of the line 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 , but still admit approximation in energy by smooth functions.
Cite
@article{arxiv.1503.06694,
title = {Singular Sets and the Lavrentiev Phenomenon},
author = {Richard Gratwick},
journal= {arXiv preprint arXiv:1503.06694},
year = {2019}
}
Comments
18 pages, to appear in Proc. Roy. Soc. Edinburgh Sect A