Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Global invertibility of Sobolev functions and the interpenetration of matter

J. M. Balla1

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.