Convex integration for Lipschitz mappings and counterexamples to regularity

Details Convex integration for Lipschitz mappings and counterexamples to regularity Convex integration for Lipschitz mappings and counterexamples to regularity

2004-02-17

arxiv.org/abs/math/0402287v1

Ann. of Math. (2), Vol. 157 (2003), no. 3, 715--742

Mathematics

Classical Analysis and ODEs

28 pages published version

Scientific paper

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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