Реферат: The limit of a locally uniformly converging sequence of analytic functions is an analytic function. Yu.G. Reshetnyak obtained a natural generalization of that in the theory of mappings with bounded distortion: the limit of every locally uniformly converging sequence of mappings with bounded distortion is a mapping with bounded distortion, and established the weak continuity of the Jacobians. In this article, similar problems are studied for a sequence of Sobolev-class homeomorphisms defined on a domain in a two-step Carnot group. We show that if such a sequence converges to some homeomorphism locally uniformly, the sequence of horizontal differentials of its terms is bounded in L_{\nu,loc}, and the Jacobians of the terms of the sequence are nonnegative almost everywhere, then the sequence of Jacobians converges to the Jacobian of the limit homeomorphism weakly in L1,loc; here ν is the Hausdorff dimension of the group.

Библиографическая ссылка: Pavlov S.V. , Vodop’yanov S.K.
Weak continuity of jacobians of Wν1-homeomorphisms on carnot groups
Eurasian Mathematical Journal. 2024. V.15. N4. P.82 – 95. DOI: 10.32523/2077-9879-2024-15-4-82-95 WOS Scopus РИНЦ OpenAlex

Даты:

Поступила в редакцию:	4 нояб. 2024 г.
Опубликована в печати:	31 янв. 2025 г.
Опубликована online:	31 янв. 2025 г.

Идентификаторы БД:

Web of science:	WOS:001420662500005
Scopus:	2-s2.0-85216945860
РИНЦ:	81523492
OpenAlex:	W4407773718

Цитирование в БД:

БД	Цитирований
Scopus	1
OpenAlex	1

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