Abstract: We prove that each homeomorphism ϕ : D → D  of Euclidean domains in Rn, n ≥ 2, belonging to the Sobolev class W1p,loc(D), where p ∈ [1,∞), and having finite distortion induces a bounded composition operator from the weighted Sobolev space L1p(D ; ω) into L1p(D) for some weight function ω : D  → (0,∞). This implies that in the cases p > n−1 and n ≥ 3 as well as p ≥ 1 and n ≥ 2 the inverse ϕ−1 : D  → D belongs to the Sobolev class W11,loc(D ), has finite distortion, and is differentiable almost everywhere in D. We apply this result to Qq,p-homeomorphisms; the method of proof also works for homeomorphisms of Carnot groups. Moreover, we prove that the class of Qq,p-homeomorphisms is completely determined by the controlled variation of the capacity of cubical condensers whose shells are concentric cubes.

Cite: Vodopʹyanov S.K.
THE REGULARITY OF INVERSES TO SOBOLEV MAPPINGS AND THE THEORY OF Qq,p-HOMEOMORPHISMS
Siberian Mathematical Journal. 2020. V.61. N6. P.1002-1038. DOI: 10.1134/S0037446620060051 WOS Scopus OpenAlex

Original: Водопьянов С.К.
О регулярности отображений, обратных к соболевским, и теория {\mathcal Q_{q,p}}-гомеоморфизмов
Сибирский математический журнал. 2020. Т.61. №6. С.1257--1299. DOI: 10.33048/smzh.2020.61.605 OpenAlex

Dates:

Submitted:	Jul 18, 2020
Accepted:	Oct 9, 2020

Identifiers:

Web of science:	WOS:000608907600005
Scopus:	2-s2.0-85099664439
OpenAlex:	W3121541088

Citing:

DB	Citing
Scopus	13
OpenAlex	15
Web of science	7

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