Invertibility and a topological property of Sobolev maps

Müller, Stefan, Spector, Scott J and Tang, Qi (1996) Invertibility and a topological property of Sobolev maps. SIAM Journal on Mathematical Analysis, 27 (4). pp. 959-976. ISSN 00361410

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Abstract

Let O be a bounded domain in Rn, let d : O¯ ¿ O¯ be a homeomorphism, and consider a function u : O¯ ¿ Rn that agrees with d on ¿O. If u is continuous and injective then u(O) = d(O). Motivated by problems in nonlinear elasticity the relationship between u(O) and d(O) is analyzed when the continuity and invertibility assumptions are weakened. Specifically maps that are continuous on almost every line and maps that lie in the Sobolev space W1,p with n - 1 < p < n are considered.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Qi Tang
Date Deposited: 06 Feb 2012 19:51
Last Modified: 04 Apr 2012 11:02
URI: http://sro.sussex.ac.uk/id/eprint/22585
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