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Convex integration for Lipschitz mappings and counterexamples to regularity

S. Muller·V. Sverak
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Abstract

We study Lispchitz solutions of partial differential relations $\nabla u\in K$, where $u$ is a vector-valued function in an open subset of $R^n$. In some cases the set of solutions turns out to be surprisingly large. The general theory is then used to construct counter-examples to regularity of solutions of Euler-Lagrange systems satisfying classical ellipticity conditions.

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S. Muller, V. Sverak. 2004-02-17. Convex integration for Lipschitz mappings and counterexamples to regularity. https://arxiv.org/abs/math/0402287

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