Mappings of finite distortion : discreteness and openness for quasi-light mappings
Hencl, Stanislav ; Koskela, Pekka
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005), p. 331-342 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2005__22_3_331_0,
     author = {Hencl, Stanislav and Koskela, Pekka},
     title = {Mappings of finite distortion : discreteness and openness for quasi-light mappings},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {22},
     year = {2005},
     pages = {331-342},
     doi = {10.1016/j.anihpc.2004.07.007},
     mrnumber = {2136727},
     zbl = {1076.30024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2005__22_3_331_0}
}

Hencl, Stanislav; Koskela, Pekka. Mappings of finite distortion : discreteness and openness for quasi-light mappings. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) pp. 331-342. doi : 10.1016/j.anihpc.2004.07.007. http://gdmltest.u-ga.fr/item/AIHPC_2005__22_3_331_0/

[1] Ball J., Global invertibility of Sobolev functions and the interpenetration of matter, Proc. Roy. Soc. Edinburgh Sect. A 88 (3-4) (1981) 315-328. | MR 616782 | Zbl 0478.46032

[2] Federer H., Geometric Measure Theory, Grundlehren Math. Wiss., vol. 153, Springer-Verlag, New York, 1969, (second edition, 1996). | MR 257325 | Zbl 0176.00801

[3] Fonseca I., Gangbo W., Degree Theory in Analysis and Applications, Clarendon Press, Oxford, 1995. | MR 1373430 | Zbl 0852.47030

[4] Gol'Dstein V., Vodop'Yanov S., Quasiconformal mappings and spaces of functions with generalized first derivatives, Sibirsk. Mat. Zh. 17 (1976) 515-531. | MR 414869 | Zbl 0353.30019

[5] Greco L., Sharp integrability of nonnegative Jacobians, Rend. Mat. 18 (1998) 585-600. | MR 1686812 | Zbl 0991.26005

[6] Heinonen J., Koskela P., Sobolev mappings with integrable dilatations, Arch. Rational Mech. Anal. 125 (1) (1993) 81-97. | MR 1241287 | Zbl 0792.30016

[7] Hencl S., Malý J., Mappings of finite distortion: Hausdorff measure of zero sets, Math. Ann. 324 (2002) 451-464. | MR 1938454 | Zbl 1017.30030

[8] Iwaniec T., Koskela P., Onninen J., Mappings of finite distortion: monotonicity and continuity, Invent. Math. 144 (2001) 507-531. | MR 1833892 | Zbl 1006.30016

[9] Iwaniec T., Martin G., Geometric Function Theory and Nonlinear Analysis, Oxford Mathematical Monographs, Clarendon Press, Oxford, 2001. | MR 1859913 | Zbl 1045.30011

[10] Iwaniec T., Šverák V., On mappings with integrable dilatation, Proc. Amer. Math. Soc. 118 (1993) 181-188. | MR 1160301 | Zbl 0784.30015

[11] Kauhanen J., Koskela P., Malý J., On functions with derivatives in a Lorentz space, Manuscripta Math. 100 (1999) 87-101. | MR 1714456 | Zbl 0976.26004

[12] Kauhanen J., Koskela P., Malý J., Mappings of finite distortion: discreteness and openness, Arch. Ration. Mech. Anal. 160 (2001) 135-151. | MR 1864838 | Zbl 0998.30024

[13] Kauhanen J., Koskela P., Malý J., Mappings of finite distortion: condition N, Michigan Math. J. 49 (2001) 169-181. | MR 1827080 | Zbl 0997.30018

[14] Kauhanen J., Koskela P., Malý J., Onninen J., Zhong X., Mappings of finite distortion: sharp Orlicz-conditions, Rev. Mat. Iberoamericana 19 (2003) 857-872. | MR 2053566 | Zbl 1059.30017

[15] Koskela P., Malý J., Mappings of finite distortion: the zero set of the Jacobian, J. Eur. Math. Soc. (JEMS) 5 (2003) 95-105. | MR 1985612 | Zbl 1025.30019

[16] Koskela P., Zhong X., Minimal assumptions for the integrability of the Jacobian, Ricerche Mat. L I (2002) 297-311. | MR 2030546 | Zbl 1096.26005

[17] Malý J., Martio O., Lusin’s condition (N) and mappings of the class W 1,n , J. Reine Angew. Math. 458 (1995) 19-36. | MR 1310951 | Zbl 0812.30007

[18] Malý J., Swanson D., Ziemer W.P., Coarea formula for Sobolev mappings, Trans. Amer. Math. Soc. 355 (2) (2003) 477-492. | MR 1932709 | Zbl 1034.46032

[19] Malý J., Ziemer W.P., Fine Regularity of Solutions of Elliptic Partial Differential Equations, Amer. Math. Soc., Providence, RI, 1997. | MR 1461542 | Zbl 0882.35001

[20] Manfredi J., Villamor E., An extension of Reshetnyak's theorem, Indiana Univ. Math. J. 47 (3) (1998) 1131-1145. | MR 1665761 | Zbl 0931.30014

[21] Reshetnyak Yu.G., Space mappings with bounded distortion, Sibirsk. Mat. Zh. 8 (1967) 629-658. | MR 994644 | Zbl 0167.06601

[22] Reshetnyak Yu.G., Space Mappings with Bounded Distortion, Transl. Math. Monographs, vol. 73, Amer. Math. Soc., 1989. | MR 994644 | Zbl 0667.30018

[23] Rickman S., Quasiregular Mappings, Ergeb. Math. Grenzgeb. (3), vol. 26, Springer-Verlag, Berlin, 1993. | MR 1238941 | Zbl 0816.30017

[24] Titus C., Young G., The extension of interiority, with some applications, Trans. Amer. Math. Soc. 103 (1962) 329-340. | MR 137103 | Zbl 0113.38001

[25] Väisälä J., Minimal mappings in Euclidean spaces, Ann. Acad. Sci. Fenn. Ser. A I 366 (1965) 1-22. | MR 178454 | Zbl 0144.22103

[26] Vuorinen M., Conformal Geometry and Quasiregular Mappings, Lecture Notes in Math., vol. 1319, Springer-Verlag, Berlin, 1988. | MR 950174 | Zbl 0646.30025