Toward the theory of the Sobolev classes with critical exponent

Authors

  • O.S. Afanas’eva Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slovyansk
  • V.I. Ryazanov Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slovyansk
  • R.R. Salimov Institute of Mathematics of the NAS of Ukraine, Kyiv

DOI:

https://doi.org/10.15407/dopovidi2019.08.003

Keywords:

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

Abstract

It is established that an arbitrary homeomorphism f in the Sobolev class

W1,n−1loc

with the outer dilatation

K0(x,f)∈Ln−1loc

is the socalled
lower Q - homeomorphism with 

Q=K0(x,f)

and the ring Q* homeomorphism with

Q∗=Kn−10(x,f)

. These results make it possible to research the local and boundary behaviors of the
mappings

W1,n−1loc

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References

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Published

21.04.2024

How to Cite

Afanas’eva, O., Ryazanov, V., & Salimov, R. (2024). Toward the theory of the Sobolev classes with critical exponent . Reports of the National Academy of Sciences of Ukraine, (8), 3–8. https://doi.org/10.15407/dopovidi2019.08.003

Issue

No. 8 (2019): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

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