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Invertibility and a topological property of Sobolev maps
journal contribution
posted on 2023-06-08, 00:17 authored by Stefan Müller, Scott J Spector, Qi TangLet 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.
History
Publication status
- Published
Journal
SIAM Journal on Mathematical AnalysisISSN
00361410Publisher
SIAM Journal of Mathematical AnalysisIssue
4Volume
27Page range
959-976ISBN
1095-7154Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes