Rigidity and lack of rigidity for solenoidal matrix fields
نویسندگان
چکیده
We study the problem of identifying conditions under which a divergence free matrix field takes values in some prescribed sets of matrices K. We treat in detail the case when K is made of two or three matrices. Our results are parallel to those on curl free matrices. In that case Ball and James showed rigidity when K is made of two matrices and Tartar proved lack of rigidity when K is made of four matrices. For our problem we prove rigidity when K is made of two matrices and lack of rigidity when is made of three. We give examples when the differential constraints are yet of a different type and present some applications to composites.
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