Young measures supported on invertible matrices

Motivated by variational problems in non-linear elasticity, we explicitly characterize the set of Young measures generated by gradients of a uniformly bounded sequence in W-1,W-infinity(Omega; R-n) where the inverted gradients are also bounded in L-infinity(Omega; R-nxn). This extends the original results due to the studies of Kinderlehrer and Pedregal. Besides, we completely describe Young measures generated by a serence of matrix-valued mappings {Y-k}(k is an element of N) subset of L-p(Omega; R-nxn), such that {Y-k(-1)}(k is an element of N) subset of L-p(Omega; R-nxn) is bounded, too, and the generating sequence satisfies the constraint det Y-k > 0.