a1 Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS
A global inverse function theorem is established for mappings u: Ω → ℝn, Ω ⊂ ℝn bounded and open, belonging to the Sobolev space W1.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.
(Received August 05 1980)
(Revised December 10 1980)
† Research partially supported by U.S. Army contract DAAG29-79-C-0086, and N.S.F. grant MCS 78-06718.