Global invertibility of Sobolev functions and the interpenetration of matter
- 1 January 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 88 (3-4) , 315-328
- https://doi.org/10.1017/s030821050002014x
Abstract
Synopsis: A global inverse function theorem is established for mappingsu: Ω → ℝn, Ω ⊂ ℝnbounded and open, belonging to the Sobolev spaceW1.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.This publication has 10 references indexed in Scilit:
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