Afanas’eva, OS 1Ryazanov, VI 2Salimov, RR 1Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Sloviansk 2Institute of Mathematics of the NAS of Ukraine, Kyiv |
Dopov. Nac. akad. nauk Ukr. 2019, 8:3-8 |
https://doi.org/10.15407/dopovidi2019.08.003 |
Section: Mathematics |
Language: Russian |
Abstract: It is established that an arbitrary homeomorphism f in the Sobolev class \[W^{1,n-1}_{loc}\] with the outer dilatation \[K_{0}(x,f) \in L^{n-1}_{loc}\] is the socalled
lower Q - homeomorphism with \[Q=K_{0} (x,f)\] and the ring Q* homeomorphism with \[Q*=K^{n-1}_{0} (x,f)\]. These results make it possible to research the local and boundary behaviors of the mappings \[W^{1,n-1}_{loc}\]
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Keywords: critical exponent, lower and ring Q homeomorphisms, outer and inner dilatations, Sobolev’s classes |
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