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On mappings with integrable dilatation


Authors: Tadeusz Iwaniec and Vladimír Šverák
Journal: Proc. Amer. Math. Soc. 118 (1993), 181-188
MSC: Primary 30C62
DOI: https://doi.org/10.1090/S0002-9939-1993-1160301-5
MathSciNet review: 1160301
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Abstract: A factorization of Stoilow's type has been obtained for mappings in $ {\mathbb{R}^2}$ with integrable dilatation.


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  • [A] L. V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand, New York, 1966. MR 0200442 (34:336)
  • [Ba] J. M. Ball, Global invertability of Sobolev functions and the interpenetration of matter, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), 315-328. MR 616782 (83f:73017)
  • [Bo1] B. V. Bojarski, Homeomorphic solutions of Beltrami systems, Dokl. Akad. Nauk USSR 102 (1955), 661-664. MR 0071620 (17:157a)
  • [Bo2] -, Generalized solutions of a system of the first order differential equations of elliptic type with discontinuous coefficients, Mat. Sb. 43 (1957), 451-503. MR 0106324 (21:5058)
  • [BI] B. V. Bojarski and T. Iwaniec, Analytical foundations of the theory of quasiconformal mappings in $ {\mathbb{R}^n}$, Ann. Acad. Sci. Fenn. Ser. A I Math. 8 (1983), 257-324. MR 731786 (85h:30023)
  • [D] G. David, Solutions de l'equation de Beltrami avec $ \vert\vert\mu \vert{\vert _\infty } = 1$, Ann. Acad. Sci. Fenn. Ser. A I Math. 13 (1988), 25-70. MR 975566 (90d:30058)
  • [L] O. Lehto, Homeomorphic solutions of a Beltrami differential equation, Festbond 70, Geburstag R. Nevanlinna, Springer, Berlin, 1966, pp. 58-65. MR 0204649 (34:4488)
  • [LV] O. Lehto and K. Virtanen, Quasiconformal mappings in the plane, Springer-Verlag, New York and Heidelberg, 1973. MR 0344463 (49:9202)
  • [Ma] J. Manfredi, Monotone Sobolev functions, preprint, University of Pittsburgh.
  • [M] A. I. Markushevich, Theory of functions of a complex variable, Prentice-Hall, Englewood Cliffs, NJ, 1967. MR 0215964 (35:6799)
  • [McA] L. F. McAuley, Monotone mappings and open mappings, Proc. of the conference in 1970, State University of New York at Binghamton.
  • [P] I. N. Pesin, Mappings that are quasiconformal in the mean, Dokl. Akad. Nauk USSR 187 (1969), 740-742; English transl., Soviet Math. (Iz. VUZ) 10 (1969), 939-941. MR 0249613 (40:2856)
  • [Re] Yu. G. Reshetnyak, Space mappings with bounded distortion, Transl. Math. Monographs, vol. 73, Amer. Math. Soc., Providence, RI, 1989. MR 994644 (90d:30067)
  • [Ri] S. Rickman, Quasiregular mappings (to appear). MR 1238941 (95g:30026)
  • [Š] V. Šverák, Regularity properties of deformations with finite energy, Arch. Rational Mech. Anal. 100 (1988), 105-127. MR 913960 (89g:73013)
  • [VG] S. K. Vodopyanov and V. M. Goldstein, Quasiconformal mappings and spaces of functions with generalized first derivatives, Siberian Math J. 17 (1977), 515-531.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1160301-5
Keywords: Quasiconformal mappings, Beltrami equation
Article copyright: © Copyright 1993 American Mathematical Society

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