Non-Lipschitz minimizers of smooth uniformly convex functionals. (English) Zbl 1106.49046
Summary: We construct non-Lipschitz minimizers of smooth, uniformly convex functionals of type \(I(u) = \int_\Omega f(Du(x))\,dx\). Our method is based on the use of null Lagrangians.
MSC:
| 49M30 | Other numerical methods in calculus of variations (MSC2010) |
| 49N60 | Regularity of solutions in optimal control |
| 49J10 | Existence theories for free problems in two or more independent variables |
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