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1995 | 31 | 1 | 255-262
Tytuł artykułu

Lebesgue measure and mappings of the Sobolev class $W^{1,n}$

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a survey of the Lusin condition (N) for $W^{1,n}$-Sobolev mappings $f:G → ℝ^n$ defined in a domain G of $ℝ^n$. Applications to the boundary behavior of conformal mappings are discussed.
Rocznik
Tom
31
Numer
1
Strony
255-262
Opis fizyczny
Daty
wydano
1995
Twórcy
autor
  • Department of Mathematics, University of Helsinki, FIN-00014 University of Helsinki, Finland
Bibliografia
  • [BI] B. Bojarski and T. Iwaniec, Analytical foundations of the theory of quasiconformal mappings in $ℝ^n$, Ann. Acad. Sci. Fenn. Ser. A I Math. 8 (1983), 257-324.
  • [C] L. Cesari, Sulle transformazioni continue, Ann. Mat. Pura Appl. 21 (1941), 157-188.
  • [G] F. W. Gehring, Rings and quasiconformal mappings in space, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 98-105.
  • [H] P. Hajłasz, Change of variables formula under minimal assumptions, Colloq. Math. 114 (1993), 93-101.
  • [HKM] J. Heinonen, T. Kilpeläinen and O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Math. Monographs, Clarendon Press, Oxford 1993.
  • [JM] P. Jones and N. G. Makarov, Density properties of harmonic measure, preprint.
  • [M] J. Malý, Hölder type quasicontinuity, to appear.
  • [MM] J. Malý and O. Martio, Lusin's condition (N) and mappings of the class $W^{1,n}$, to appear.
  • [MZ] O. Martio and W. P. Ziemer, Lusin's condition (N) and mappings with non-negative Jacobians, Michigan Math. J., to appear.
  • [Mu] S. Müller, Higher integrability of determinants and weak convergence in $L^1$, J. Reine Angew. Math. 412 (1990), 20-34.
  • [NP] R. Näkki and B. Palka, Boundary angles, cusps and conformal mappings, Complex Variables Theory Appl. 5 (1986), 165-180.
  • [P] S. P. Ponomarev, Examples of homeomorphisms in the class $ACTL^p$ which do not satisfy the absolute continuity condition of Banach, Dokl. Akad. Nauk SSSR 201 (1971), 1053-1054 (in Russian).
  • [RR] T. Radó and P. V. Reichelderfer, Continuous Transformations in Analysis, Springer 1955.
  • [Rei] H. M. Reimann, On the absolute continuity of a surface representation, Comment. Math. Helv. 46 (1971), 44-47.
  • [Res1] Yu. G. Reshetnyak, The condition (N) for $W^1_{n,loc}$ space mappings, Sibirsk. Mat. Zh. 28 (1987), 149-153 (in Russian).
  • [Res2] Yu. G. Reshetnyak, Space Mappings with Bounded Distortion, Transl. Math. Monographs 73, Amer. Math. Soc., 1989.
  • [S] S. Saks, Theory of the Integral, Warsaw, 1937.
  • [V] J. Väisälä, Quasiconformal maps and positive boundary measure, Analysis 9 (1989), 205-216.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv31z1p255bwm
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