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DOI: 10.23671/VNC.2017.2.6507

# On the Power Order of Growth of Lower $$Q$$-Homeomorphisms

Salimov R. R.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 2.
Abstract:
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 $$W^{1,\varphi}_{\rm loc}$$ in $$\mathbb{R}^n$$, $$n\geqslant 3$$, under conditions of the Calderon type on $$\varphi$$ and, in particular, to Sobolev classes $$W_{\rm loc}^{1,p},$$ $$p>n-1$$. We give also an example of a homeomorphism demonstrating that the established order of growth is precise.
Keywords: $$p$$-modulus, $$p$$-capacity, lower $$Q$$-homeomorphisms, mappings of finite distortion, Sobolev class, Orlicz-Sobolev class.
For citation: Salimov R. R. On the Power Order of Growth of Lower $$Q$$-Homeomorphisms. Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 36-48. DOI 10.23671/VNC.2017.2.6507