Geodesic
On the power order of growth of lower $Q$-homeomorphisms
Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 2, pp. 36-48

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In the present paper we investigate the asymptotic behavior of $Q$-homeomorphisms with respect to a $p$-modulus at a point. The sufficient conditions on $Q$ under which a mapping has a certain order of growth are obtained. We also give some applications of these results to Orlicz–Sobolev classes $W^{1,\varphi}_{\mathrm{loc}}$ in $\mathbb{R}^n$, $n\geqslant 3$, under conditions of the Calderon type on $\varphi$ and, in particular, to Sobolev classes $W_{\mathrm{loc}}^{1,p},$ $p>n-1$. We give also an example of a homeomorphism demonstrating that the established order of growth is precise. 
@article{VMJ_2017_19_2_a4,
     author = {R. R. Salimov},
     title = {On the power order of growth of lower $Q$-homeomorphisms},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {36--48},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2017_19_2_a4/}
}
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R. R. Salimov. On the power order of growth of lower $Q$-homeomorphisms. Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 2, pp. 36-48. http://geodesic.mathdoc.fr/item/VMJ_2017_19_2_a4/