Invertibility and a topological property of Sobolev maps
journal contribution
posted on 2023-06-08, 00:17authored byStefan Müller, Scott J Spector, Qi Tang
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.