On mappings in the Orlicz-Sobolev classes

作者: Denis Kovtonyuk , Evgeny Sevost ' yanov , Vladimir Ryazanov , Ruslan Salimov

DOI:

关键词:

摘要: Under a condition of the Calderon type on ', we show that continuous mappings f in W 1;' loc , particular, 2 1;p for p > n 1 have (N)-property by Lusin a.e. hyperplane. It is proved this basis under given ' homeomorphisms with nite distortion and, are so- called lower Q-homeomorphisms where Q(x) equal to its outer dilatation Kf (x). This makes possible apply our theory boundary behavior Orlicz-Sobolev classes.

参考文章(115)
Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov, Homeomorphisms with Finite Mean Dilatations Springer New York. pp. 237- 255 ,(2009) , 10.1007/978-0-387-85588-2_12
Joseph Hesse, A p-extremal length and p-capacity equality Arkiv för Matematik. ,vol. 13, pp. 131- 144 ,(1975) , 10.1007/BF02386202
S. K. Vodop'yanov, Mappings with bounded distortion and with finite distortion on Carnot groups Siberian Mathematical Journal. ,vol. 40, pp. 644- 677 ,(1999) , 10.1007/BF02675667
Luigi Ambrosio, Metric space valued functions of bounded variation Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze. ,vol. 17, pp. 439- 478 ,(1990)
Christopher J. Bishop, QUASICONFORMAL MAPPINGS WHICH INCREASE DIMENSION Annales Academiae Scientiarum Fennicae. Series A1. Mathematica. ,vol. 24, pp. 397- 407 ,(1999)
Jan Maly, Olli Martio, Lusin's condition (N) and mappings of the class W1, n. Crelle's Journal. ,vol. 458, pp. 19- 36 ,(1995)
A. Vasil'ev, MODULI OF FAMILIES OF CURVES AND QUASICONFORMAL MAPPINGS Journal of Mathematical Sciences. ,vol. 106, pp. 3487- 3517 ,(2001) , 10.1023/A:1011923930088
Uri Srebro, Eduard Yakubov, O. Martio, Vladimir Ryazanov, Moduli in Modern Mapping Theory ,(2009)
Miodrag Perović, Isolated singularity of the mean quasiconformal mappings Romanian-Finnish Seminar on Complex Analysis. pp. 212- 214 ,(1979) , 10.1007/BFB0079494
O. Martio, S. Rickman, J. Väisälä, Definitions for quasiregular mappings Annales Academiae Scientiarum Fennicae Series A I Mathematica. ,vol. 1969, pp. 1- 40 ,(1969) , 10.5186/AASFM.1969.448