Mappings with dilatation in Orlicz spaces

• Autores: Jana Björn
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 53, Fasc. 3, 2002, págs. 303-312
• Idioma: inglés
• Títulos paralelos:
  • Mapeos con dilatación en espacios de Orlicz
• Enlaces
  • Texto completo
• Resumen

  • We prove openness and discreteness for nonconstant mappings belonging to $W^{1,n}_{loc} (\Omega,\mathbb{R}^n)\geq 3$, with dilatation in certain Orlicz spaces which are strictly larger then all $L^p_{loc}(\Omega), p>n-1$. This result contributes to decreasing the gap between known results and a conjecture of Iwaniec and \v{S}verák.

• Referencias bibliográficas
  • J. Ball, Global invertibility of Sobolev functions and the interpenetration of matter, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), 315–328.
  • J. Heinonen and P. Koskela, Sobolev mappings with integrable dilatations, Arch. Rational Mech. Anal. 125 (1993), 81–97.
  • S. Hencl and J. Malý, Mappings of finite distortion: Hausdorff measure of zero sets, Preprint 2001.
  • T. Iwaniec and V. Šverák, On mappings with integrable dilatation, Proc. Amer. Math. Soc. 118 (1993), 181–188.
  • T. Iwaniec, P. Koskela, and J. Onninen, Mappings of finite distortion: monotonicity and continuity, Invent. Math. 144 (2001), 507–531.
  • J. Kauhanen, P. Koskela, and J. Malý, Mappings of finite distortion: discreteness and openness, Arch. Rational Mech. Anal. 160 (2001), 135–151.
  • R. O’Neil, Fractional integration in Orlicz spaces, I, Trans. Amer. Math. Soc. 115 (1965), 300–328.
  • J. Onninen, Orlicz capacities and Hausdorff measures in metric spaces, (in preparation).
  • Yu.G. Reshetnyak, Space mappings with bounded distortion, Sibirsk. Mat. Zh. 8 (1967), 629–658 (in Russian), Siberian Math. J. 3 (1967), 466–486...
  • Yu.G. Reshetnyak, Spatial mappings with bounded distortion, Nauka, Moscow, 1982 (in Russian), Amer. Math. Soc., Providence, RI, 1989 (English...
  • S. Rickman, Quasiregular mappings, Springer-Verlag, Berlin, 1993.
  • C.J. Titus and G.S. Young, The extension of interiority with some applications, Trans. Amer. Math. Soc. 103 (1962), 329–340.
  • E. Villamor and J.J. Manfredi, An extension of Reshetnyak’s theorem, Indiana Univ. Math. J. 47 (1998), 1131–1145.
  • W\.P. Ziemer, Weakly differentiable functions, Sobolev spaces and functions of bounded variation, Springer-Verlag, New York, 1989.