On $p$-modulus estimates in Orlicz-Sobolev classes

Abstract

Under a condition of the Calderon type on $\phi$, we show that a homeomorphism $f$ of finite distortion in $W_{\mathrm{loc}}^{1,\phi }$ and, in particular, $f\in W_{\mathrm{loc}}^{1,q}$ for $q>n-1$ in ${\mathbb{R}}^n$, $n\ge 3$, is a lower $Q$-homeomorphisms with respect to the $p$-modulus with ${\left[K_{I,\alpha }(x,f)\right]}^{\beta }$, $p>n-1$ and a ring $Q_{\ast }$-homeomorphism with respect to the $\frac{p}{p-n+1}$-modulus with $Q_{\ast }(x)=K_{I,\alpha }(x,f)$ where $K_{I,\alpha }(x,f)$ is its inner $\alpha$-dilatation and $\alpha =\frac{p}{p-n+1}$, $\beta =\frac{p-n+1}{n-1}$.

The paper has been withdrawn as it is being merged into a joint paper with additional authors

References in corpus (1)

• On mappings in the Orlicz-Sobolev classes