We consider the following question: given a set of matrices Jf with no rank-one connections, does it support a nontrivial Young measure limit of gradients? Our main results are these: (a) a Young measure can be supported on four incompatible matrices; (b) in two space dimensions, a Young measure cannot be supported on finitely many incompatible elastic wells; (c) in three or more space dimensions, a Young measure can be supported on three incompatible elastic wells; and (d) if k supports a nontrivial Young measure with mean value 0, then the linear span of Jf must contain a matrix of rank one.
|Original language||English (US)|
|Number of pages||36|
|Journal||Proceedings of the Royal Society of Edinburgh: Section A Mathematics|
|State||Published - Jan 1 1994|