Toward the theory of the Sobolev classes with critical exponent

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
Section: Mathematics
Language: Russian
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 \[W^{1,n-1}_{loc}\]





Keywords: critical exponent, lower and ring Q homeomorphisms, outer and inner dilatations, Sobolev’s classes

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