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Global invertibility of Sobolev functions and the interpenetration of matter

Published online by Cambridge University Press:  14 November 2011

J. M. Ball
J. M. Ball
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS
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Synopsis

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 3-4 , 1981 , pp. 315 - 328
Copyright
Copyright © Royal Society of Edinburgh 1981

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