Neohookean deformations of annuli in the higher dimensional Euclidean space

Let $n\ge 2$ be an integer and assume that $\mathbb{A}=\{x\in {\mathbf{R}}^n:1<\mathrm{\mid }x\mathrm{\mid }<R\}$ and $\A_\ast = {y \in $\mathbf{R}$^n: 1 < |y| < R_\ast}$betwoannuliinEuclideanspace$$\mathbf{R}$^n$. Assume that $\mathcal{F}(\text{A},{\text{A}}_{\ast })$ (resp. $\mathcal{R}(\text{A},{\text{A}}_{\ast })$) be the class of all orientation preserving (resp. radial) homeomorphisms $h : \A \mapsto \A_\ast$intheSobolevspace$$\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.