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A one-dimensional variational problem with continuous Lagrangian and singular minimizer
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Gratwick, Richard and Preiss, David (2011) A one-dimensional variational problem with continuous Lagrangian and singular minimizer. Archive for Rational Mechanics and Analysis, Vol.202 (No.1). pp. 177-211. doi:10.1007/s00205-011-0413-3 ISSN 0003-9527.
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Official URL: http://dx.doi.org/10.1007/s00205-011-0413-3
Abstract
We construct a continuous Lagrangian, strictly convex and superlinear
in the third variable, such that the associated variational problem has a Lipschitz
minimizer which is non-differentiable on a dense set. More precisely, the upper
and lower Dini derivatives of the minimizer differ by a constant on a dense (hence
second category) set. In particular, we show that mere continuity is an insufficient
smoothness assumption for Tonelli’s partial regularity theorem.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Lagrangian functions, Variational principles | ||||
Journal or Publication Title: | Archive for Rational Mechanics and Analysis | ||||
Publisher: | Springer | ||||
ISSN: | 0003-9527 | ||||
Official Date: | October 2011 | ||||
Dates: |
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Volume: | Vol.202 | ||||
Number: | No.1 | ||||
Page Range: | pp. 177-211 | ||||
DOI: | 10.1007/s00205-011-0413-3 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 18 December 2015 | ||||
Date of first compliant Open Access: | 18 December 2015 |
Data sourced from Thomson Reuters' Web of Knowledge
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