# Neohookean deformations of annuli in the higher dimensional Euclidean space

## TL;DR

This paper investigates Neohookean deformations of annuli in higher-dimensional Euclidean spaces, extending previous results on energy-minimizing homeomorphisms within Sobolev spaces.

## Contribution

It generalizes earlier work by Iwaniec and Onninen to higher dimensions, analyzing deformations of annuli under Neohookean energy constraints.

## Key findings

- Characterization of energy-minimizing deformations
- Extension of results to higher dimensions
- Conditions for existence of homeomorphisms

## Abstract

Let $n\ge 2$ be an integer and assume that $\mathbb{A}=\{x\in\mathbf{R}^n:1<|x|<R\}$ and $\A_\ast = \{y \in \mathbf{R}^n: 1 < |y| < R_\ast\}$ be two annuli in Euclidean space $\mathbf{R}^n$. Assume that $\mathcal{F}(\A, \A_\ast)$ (resp. $\mathcal{R}(\A, \A_\ast)$) be the class of all orientation preserving (resp. radial) homeomorphisms $h : \A \mapsto \A_\ast$ in the Sobolev space $\mathcal{W} ^{1,n}(\A, \A_\ast)$ which keep the boundary circles in the same order. In this paper, we extended the corresponding results of Iwaniec and Onninen which was published in {\it Math. Ann.} Vol. 348, 2010.