INVERTIBILITY AND A TOPOLOGICAL PROPERTY OF SOBOLEV MAPS

Let Omega be a bounded domain in R(n), let d : <(Omega)over bar> --> < (Omega)over bar> be a homeomorphism, and consider a function u : <(Ome ga)over bar> --> R(n) that agrees with d on partial derivative Omega. if u is continuous and injective then u(Omega) = d(Omega). Motivated b y problems in nonlinear elasticity the relationship between u(Omega) a nd d(Omega) when the continuity and invertibility assumptions are weak ened. Specifically maps that are continuous on almost every line and m aps that lie in the Sobolev space W-1,W-p with n - 1 < p < n are consi dered.