a1 Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K. (On leave from MFF UK, Charles University, Prague, Czechoslovakia)
We consider variational integrals
defined for (sufficiently regular) functions u: Ω→Rm. Here Ω is a bounded open subset of Rn, Du(x) denotes the gradient matrix of u at x and f is a continuous function on the space of all real m × n matrices Mm × n. One of the important problems in the calculus of variations is to characterise the functions f for which the integral I is lower semicontinuous. In this connection, the following notions were introduced (see , , ).
(Received November 13 1991)