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Authors: ELENA AFANASEVA, ANATOLY GOLBERG, RUSLAN SALIMOV.
DOI: 10.24193/subbmath. 2022.2.15
Published Online: 2022-06-10
Published Print: 2022-06-30
pp. 403-420
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Abstract: We study the distortion features of ho-meo-mor-phisms of Sobolev class $W^{1,1}_{ m loc}$ admitting integrability for $p$-outer dilatation. We show that such mappings belong to $W^{1,n-1}_{ m loc},$ are differentiable almost everywhere and possess absolute continuity in measure. In addition, such mappings are both ring and lower $Q$-homeomorphisms with appropriate measurable functions $Q.$ This allows us to derive various distortion results like Lipschitz, H"older, logarithmic H"older continuity, etc. We also establish a weak bounded variation property for such class of homeomorphisms.
Key words: Sobolev classes, Lusin''s (N)-property, finitely Lipschitz mappings, ring Q-homeomorphisms, lower Q-homeomorphisms, Lipschitz continuity, Hölder continuity, bounded variation.
Mathematics Subject Classification (2010): 30C65, 26B35, 46E35
