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We study solutions of first order partial differential relations , where
is a Lipschitz map and is a bounded set in matrices, and extend Gromov’s theory of convex integration in two ways. First, we allow for additional
constraints on the minors of and second we replace Gromov’s −convex hull by the (functional) rank-one convex hull. The latter can be much larger than the former and this has important consequences for the existence of ‘wild’ solutions to elliptic systems. Our work was originally...
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