Limits of Sobolev Homeomorphisms in Nonlinear Elasticity

Abstract: Limits of Sobolev homeomorphisms naturally appear in geometric function theory, calculus of variations, and continuum mechanics. In this talk, we discuss the properties of mappings that are essential for elastic deformations, focusing on aspects such as continuity, injectivity, and differentiability, as well as Lusin’s (N) and (N-1) conditions. We also consider variational problems of nonlinear elasticity, where admissible deformations are given by limits of Sobolev homeomorphisms, and discuss the existence of minimizers.