Functional and analytic properties of a class of mappings in quasi-conformal analysis

Functional and analytic properties of a class of mappings in quasi-conformal analysis Full article

Journal

Izvestiya Mathematics
ISSN: 1064-5632

Output data

Year: 2021, Volume: 85, Number: 5, Pages: 883-931 Pages count : 49 DOI: 10.1070/IM9082

Tags

Capacity; Composition operator; Modulus of a condenser; Quasi-conformal analysis; Sobolev space

Authors

Vodopyanov S.K. ¹ , Tomilov A.O. ¹

Affiliations

1	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation

We define a two-index scale (Formula presented) of homeomorphisms of spatial domains in ℝn, the geometric description of which is determined by the control of the behaviour of the q-capacity of condensers in the target space in terms of the weighted p-capacity of condensers in the source space. We obtain an equivalent functional and analytic description of (Formula presented) based on the properties of the composition operator (from weighted Sobolev spaces to non-weighted ones) induced by the inverses of the mappings in (Formula presented). When q = p = n, the class of mappings (Formula presented) coincides with the set of so-called Q-homeomorphisms which have been studied extensively in the last 25 years. © 2021 Russian Academy of Sciences (DoM) and London Mathematical Society

Vodopyanov S.K. , Tomilov A.O.
Functional and analytic properties of a class of mappings in quasi-conformal analysis
Izvestiya Mathematics. 2021. V.85. N5. P.883-931. DOI: 10.1070/IM9082 WOS Scopus OpenAlex

Водопьянов С.К. , Томилов А.О.
Функциональные и аналитические свойства одного класса отображений квазиконформного анализа
Известия Российской академии наук. Серия математическая. 2021. Т.85. №5. С.58-109. DOI: 10.4213/im9082 OpenAlex

Web of science:	WOS:000714745800001
Scopus:	2-s2.0-85120171195
OpenAlex:	W3097403566

DB	Citing
Scopus	9
OpenAlex	12
Web of science	9