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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
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] Lars V. Ahlfors, Lectures on quasiconformal mappings, Manuscript prepared with the assistance of Clifford J. Earle, Jr. Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. MR 0200442
  • [Ba] J. M. Ball, Global invertibility of Sobolev functions and the interpenetration of matter, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), no. 3-4, 315–328. MR 616782, 10.1017/S030821050002014X
  • [Bo1] B. V. Boyarskiĭ, Homeomorphic solutions of Beltrami systems, Dokl. Akad. Nauk SSSR (N.S.) 102 (1955), 661–664 (Russian). MR 0071620
  • [Bo2] B. V. Boyarskiĭ, Generalized solutions of a system of differential equations of first order and of elliptic type with discontinuous coefficients, Mat. Sb. N.S. 43(85) (1957), 451–503 (Russian). MR 0106324
  • [BI] B. Bojarski and T. Iwaniec, Analytical foundations of the theory of quasiconformal mappings in 𝑅ⁿ, Ann. Acad. Sci. Fenn. Ser. A I Math. 8 (1983), no. 2, 257–324. MR 731786, 10.5186/aasfm.1983.0806
  • [D] Guy David, Solutions de l’équation de Beltrami avec \Vert𝜇\Vert_{∞}=1, Ann. Acad. Sci. Fenn. Ser. A I Math. 13 (1988), no. 1, 25–70 (French). MR 975566, 10.5186/aasfm.1988.1303
  • [L] Olli Lehto, Homeomorphic solutions of a Beltrami differential equation, Festband 70. Geburtstag R. Nevanlinna, Springer, Berlin, 1966, pp. 58–65. MR 0204649
  • [LV] O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, 2nd ed., Springer-Verlag, New York-Heidelberg, 1973. Translated from the German by K. W. Lucas; Die Grundlehren der mathematischen Wissenschaften, Band 126. MR 0344463
  • [Ma] J. Manfredi, Monotone Sobolev functions, preprint, University of Pittsburgh.
  • [M] A. I. Markushevich, Theory of functions of a complex variable. Vol. III, Revised English edition, translated and edited by Richard A. Silverman, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0215964
  • [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 which are quasiconformal in the mean, Dokl. Akad. Nauk SSSR 187 (1969), 740–742 (Russian). MR 0249613
  • [Re] Yu. G. Reshetnyak, Space mappings with bounded distortion, Translations of Mathematical Monographs, vol. 73, American Mathematical Society, Providence, RI, 1989. Translated from the Russian by H. H. McFaden. MR 994644
  • [Ri] Seppo Rickman, Quasiregular mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 26, Springer-Verlag, Berlin, 1993. MR 1238941
  • [Š] Vladimír Šverák, Regularity properties of deformations with finite energy, Arch. Rational Mech. Anal. 100 (1988), no. 2, 105–127. MR 913960, 10.1007/BF00282200
  • [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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Keywords: Quasiconformal mappings, Beltrami equation
Article copyright: © Copyright 1993 American Mathematical Society