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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.
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.
Language: Russian Download the full text  
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
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