Geodesic
Weak continuity of Jacobians of $W_\nu^1$-homeomorphisms on Carnot groups
Eurasian mathematical journal, Tome 15 (2024) no. 4, pp. 82-95 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $L_{\nu,\mathrm{loc}}$, 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 $L_{\nu,\mathrm{loc}}$; here $\nu$ is the Hausdorff dimension of the group. 
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S. V. Pavlov; S. K. Vodopyanov. Weak continuity of Jacobians of $W_\nu^1$-homeomorphisms on Carnot groups. Eurasian mathematical journal, Tome 15 (2024) no. 4, pp. 82-95. http://geodesic.mathdoc.fr/item/EMJ_2024_15_4_a4/

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