Abstract: 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.

Cite: 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

Dates:

Submitted:	Nov 4, 2024
Published print:	Jan 31, 2025
Published online:	Jan 31, 2025

Identifiers:

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

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Scopus	2
OpenAlex	3
Web of science	2

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