Geodesic
Sufficient conditions for local quasiconformality of mappings with bounded distortion
Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 437-445
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Sufficient conditions for a mapping $f(x)$ with bounded distortion to be a local homeomorphism are established in terms of estimates of the oscillation of its normalized Jacobi matrix $$ f'(x)/\lvert\det f'(x)\rvert^{1/n}. $$ The results obtained are used in the description of properties of the solutions of the system of partial differential equations $$ f'(x)=K(x)\lvert\det f'(x)\rvert^{1/n}, $$ where $K(x)$ is a given matrix-valued function. 
@article{SM_1994_78_2_a10,
     author = {I. V. Zhuravlev},
     title = {Sufficient conditions for local quasiconformality of mappings with bounded distortion},
     journal = {Sbornik. Mathematics},
     pages = {437--445},
     year = {1994},
     volume = {78},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_2_a10/}
}
TY  - JOUR
AU  - I. V. Zhuravlev
TI  - Sufficient conditions for local quasiconformality of mappings with bounded distortion
JO  - Sbornik. Mathematics
PY  - 1994
SP  - 437
EP  - 445
VL  - 78
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1994_78_2_a10/
LA  - en
ID  - SM_1994_78_2_a10
ER  - 
%0 Journal Article
%A I. V. Zhuravlev
%T Sufficient conditions for local quasiconformality of mappings with bounded distortion
%J Sbornik. Mathematics
%D 1994
%P 437-445
%V 78
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1994_78_2_a10/
%G en
%F SM_1994_78_2_a10
I. V. Zhuravlev. Sufficient conditions for local quasiconformality of mappings with bounded distortion. Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 437-445. http://geodesic.mathdoc.fr/item/SM_1994_78_2_a10/

[1] Reshetnyak Yu. G., Prostranstvennye otobrazheniya s ogranichennym iskazheniem, Nauka, Novosibirsk, 1982 | MR

[2] Alfors L., Preobrazovaniya Mebiusa v mnogomernom prostranstve, Mir, M., 1986 | MR

[3] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR

[4] Reshetnyak Yu. G., Teoremy ustoichivosti v geometrii i analize, Nauka, Novosibirsk, 1982 | MR

[5] Martio O., Rickman S., Väisälä Ju., “Topological and metric properties of quasiregular mappings”, Ann. Acad. Sci. Fenn., Ser. A1, 1971, no. 488, 1–31 | MR

[6] Zorich V. A., “Teorema Lavrenteva o kvazikonformnykh otobrazheniyakh prostranstva”, Matem. sb., 74(116):3 (1967), 417–433 | MR | Zbl

[7] Zhuravlev I. V., “Vosstanovlenie otobrazheniya po normirovannoi matritse Yakobi”, DAN SSSR, 317:3 (1991), 546–549 | MR | Zbl

[8] Zhuravlev I. V., “O vosstanovlenii otobrazheniya s ogranichennym iskazheniem po kharakteristike”, Tez. dokl. VII nauchn. konf. VolGU (Volgograd, apr. 1990 g.), Volgograd, 1990, 88–89

[9] De Ram Zh., Differentsiruemye mnogoobraziya, Il, M., 1956