Abstract
Let Ω, Ω′ ⊂ ℝn be bounded domains and let fm: Ω → Ω′ be a sequence of homeomorphisms with positive Jacobians Jfm > 0 a.e. and prescribed Dirichlet boundary data. Let all fm satisfy the Lusin (N) condition and supm ∫Ω( |D fm|n - 1 + A( |cof D fm|) + φ(Jf)) < ∞, where A and φ are positive convex functions. Let f be a weak limit of fm in W1,n−1. Provided certain growth behaviour of A and φ, we show that f satisfies the (INV) condition of Conti and De Lellis, the Lusin (N) condition, and polyconvex energies are lower semicontinuous.
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