Regularity of inverses of Sobolev deformations with finite surface energy

摘要

Let u be a Sobolev W-1,W-P map from a bounded open set Omega subset of R-n to R-n. We assume u to satisfy some invertibility properties that are natural in the context of nonlinear elasticity, namely, the topological condition INV and the orientation-preserving constraint det Du > 0. These deformations may present cavitation, which is the phenomenon of void formation. We also assume that the surface created by the cavitation process has finite area. If p > n - 1, we show that a suitable defined inverse of u is a Sobolev map. A partial result is also given for the critical case p = n - 1. The proof relies on the techniques used in the study of cavitation. (C) 2014 Elsevier Inc. All rights reserved.