On the convergence of mappings with $k$-finite distortion
Problemy analiza, Tome 7 (2018) no. 3, pp. 88-100.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that a locally uniform limit of a sequence of homeomorphisms with finite $k$-distortion is also a mapping with finite $k$-distortion. We obtain also an estimation for the distortion coefficient of the limit mapping.
Keywords: mapping with $k$-finite distortion, passing to the limit, differential form.
Mots-clés : distortion coefficient
@article{PA_2018_7_3_a7,
     author = {N. A. Kudryavtseva and S. K. Vodopyanov},
     title = {On the convergence of mappings with   $k$-finite distortion},
     journal = {Problemy analiza},
     pages = {88--100},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2018_7_3_a7/}
}
TY  - JOUR
AU  - N. A. Kudryavtseva
AU  - S. K. Vodopyanov
TI  - On the convergence of mappings with   $k$-finite distortion
JO  - Problemy analiza
PY  - 2018
SP  - 88
EP  - 100
VL  - 7
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2018_7_3_a7/
LA  - en
ID  - PA_2018_7_3_a7
ER  - 
%0 Journal Article
%A N. A. Kudryavtseva
%A S. K. Vodopyanov
%T On the convergence of mappings with   $k$-finite distortion
%J Problemy analiza
%D 2018
%P 88-100
%V 7
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2018_7_3_a7/
%G en
%F PA_2018_7_3_a7
N. A. Kudryavtseva; S. K. Vodopyanov. On the convergence of mappings with   $k$-finite distortion. Problemy analiza, Tome 7 (2018) no. 3, pp. 88-100. http://geodesic.mathdoc.fr/item/PA_2018_7_3_a7/

[1] Baykin A. N., Vodop'yanov S. K., “Capacity estimates, Liouville's theorem, and singularity removal for mappings with bounded $(p, q)$-distortion”, Sib. Math. J., 56:2 (2015), 237–261 | DOI | MR | Zbl

[2] Brooks J. K., Chacon R. V., “Continuity and compactness of measures”, Adv. Math., 37:1 (1980), 16–26 | DOI | MR | Zbl

[3] Federer H., Geometric Measure Theory, Springer-Verlag, 1969 | MR | Zbl

[4] Fusco N., Moscariello G., Sbordone C., “The limit of $W^{1,1}$ homeomorphisms with finite distortion”, Calc. Var., 33:3 (2008), 377–390 | DOI | MR | Zbl

[5] Gehring F. W., Iwaniec T., “The limit of mappings with finite distortion”, Ann. Acad. Sci. Fenn. Math., 24 (1999), 253–264 | MR | Zbl

[6] Hajłash P., “Change of variables formula under minimal assumptions”, Colloq. Math., 64:1 (1993), 93–101 | DOI | MR | Zbl

[7] Iwaniec T., Šverák V., “On mappings with integrable dilatation”, Proc. Amer. Math. Soc., 118:1 (1993), 181–188 | DOI | MR | Zbl

[8] Reshetnyak Yu. G., Space Mappings with Bounded Distortion, Amer. Math. Soc., 1989 | MR | Zbl

[9] Stein E. M., Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970 | MR | Zbl

[10] Troyanov M., Vodop'yanov S. K., “Liouville type theorems for mappings with bounded (co)-distortion”, Ann. Inst. Fourier, Grenoble, 52:6 (2001), 1753–1784 | DOI | MR

[11] Vodop'yanov S. K., “Closure of classes of mappings with bounded distortion on Carnot groups”, Sib. Adv. Math., 14:1 (2004), 84–125 | MR | Zbl

[12] Vodop'yanov S. K., “Spaces of differential forms and maps with controlled distortion”, Izvestiya: Mathematics, 74:4 (2010), 663–689 | DOI | MR | Zbl

[13] Vodop'yanov S. K., “Regularity of mappings inverse to Sobolev mappings”, Sbornik: Mathematics, 203:10 (2012), 1383–1410 | DOI | MR | Zbl

[14] Vodop'yanov S. K., “Quasiconformal analysis of two-indexed scale of spatial mappings and its applications”, Abstracts International Conference on Complex Analysis and its Applications (Krasnodar, June, 02–09, 2018), 25–27

[15] Vodop'yanov S. K., Gol'dstein V. M., “Quasiconformal mappings and spaces of functions with generalized first derivatives”, Sib. Math. J., 17:3 (1976), 399–411 | DOI

[16] Vodop'yanov S. K., Kudryavtseva N. A., “On the convergence of mappings with k-finite distortion”, Math. Notes, 102:5–6 (2017), 878–883 | DOI | MR | Zbl

[17] Vodopyanov S. K., Molchanova A. O., “Lower semicontinuity of mappings with bounded $(\theta,1)$-weighted $(p,q)$-distortion”, Sib. Math. J., 57:5 (2016), 778–787 | DOI | MR | Zbl