Year: 2019
Type: preprint
Abstract: In this paper we study geometric aspects of Ball's classes in the context of nonlinear elasticity problems. The suggested approach is based on the characterization of Ball's classes $A_{q,q'}(Ω)$ in terms of composition operators on Sobolev spaces. This characterization allows us to obtain the volume compression (distortion) estimates of topological mappings of Ball's classes. We prove also that Sobolev homeomorphisms of Ball's classes which possess the Luzin $N$-property are absolutely continuous with respect to capacity.
Source: arXiv (Cornell University)
Authors: Gol'dshtein, Vladimir, Ukhlov, Alexander
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4672610642
OpenAlex ID: W3044217662