Year: 2015
Type: preprint
Abstract: We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general of the form of a standard Lipschitz "variation". Part of this investigation, but of interest in its own right, is an example of a nowhere locally Lipschitz minimizer which serves as a counter-example to any putative Tonelli partial regularity statement. Under these low assumptions we find it nonetheless remains possible to derive necessary conditions for minimizers, in terms of approximate continuity and equality of the one-sided derivatives.
Source: arXiv (Cornell University)
Author: Gratwick, Richard
Institution: University of Edinburgh
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953374882