Global invertibility of Sobolev functions and the interpenetration of matter

Synopsis A global inverse function theorem is established for mappings u : Ω → ℝ n , Ω ⊂ ℝ n bounded and open, belonging to the Sobolev space W 1.p (Ω), p > n . The theorem is applied to the pure displacement boundary value problem of nonlinear elastostatics, the conclusion being that there is no interpenetration of matter for the energy-minimizing displacement field.