Restrictions on microstructure

Kaushik Bhattacharya, Nikan B. Firoozye, Richard D. James, Robert V. Kohn

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)843-878
Number of pages36
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Issue number5
StatePublished - 1994

ASJC Scopus subject areas

  • General Mathematics


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