Mathematics – Classical Analysis and ODEs
Scientific paper
2010-02-16
Mathematics
Classical Analysis and ODEs
27 pages, second author added, introductory material changed, minor typos corrected, some cross-references re-formatted, some
Scientific paper
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.
Gratwick Richard
Preiss David
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