On the degenerate Beltrami equation

Transactions of the American Mathematical Society

Volumn 357, Issue 3, 2005, Pages 875-900

  Gutlyanskii V ^a   Martio, O ^b   Sugawa, T ^c   Vuorinen, M ^d  

^a INSTITUTE OF APPLIED MATHEMATICS AND MECHANICS   (Ukraine)

^b UNIVERSITY OF HELSINKI   (Finland)

^c HIROSHIMA UNIVERSITY   (Japan)

^d UNIVERSITY OF TURKU   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14844337558     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-04-03708-0     Document Type: Article

References (25)

1. L. V. Ahlfors, Lectures on Quasiconformal Mappings, van Nostrand, 1966. MR0200442 (34:336)
2. C. Andreian Cazacu, Influence of the orientation of the characteristic ellipses on the properties of the quasiconformal mappings, Proceedings of the Romanian-Finnish Seminar on Teichmüller Spaces and Quasiconformal Mappings (Braşov, 1969), Publ. House of the Acad. of the Socialist Republic of Romania, Bucharest, 1971, pp. 65-85. MR0318478 (47:7025)
3. K. Astala, T. Iwaniec, P. Koskela, and G. J. Martin, Mappings of BMO-bounded distortion, Math. Ann. 317 (2000), 703-726. MR1777116 (2001i:30016)
4. P. P. Belinskiǐ, General properties of quasiconformal mappings (Russian), Izdat. "Nauka" Sibirsk. Otdel., Novosibirsk, 1974. MR0407275 (53:11054)
5. L. Bers, Uniformisation by Beltrami equation, Commun. in Pure and Appl. Math. 14 (1961), 215-228. MR0132175 (24:A2022)
6. M. A. Brakalova and J. A. Jenkins, On solutions of the Beltrami equation, J. Anal. Math. 76 (1998), 67-92. MR1676936 (2000h:30029)
7. Z.-G. Chen, Estimates on μ(z)-homeomorphisms of the unit disk, Israel J. Math. 122 (2001), 347-358. MR1826507 (2002b:30020)
8. ∞ = 1, Ann. Acad. Sci. Fenn. Ser. A I Math. 13 (1988), 25-70. MR0975566 (90d:30058)
9. F. W. Gehring, A remark on the moduli of rings, Comment. Math. Helv. 36 (1962), 42-46. MR0140682 (25:4097)
10. Y. Gotoh and M. Taniguchi, A condition of quasiconformal extendability, Proc. Japan Acad. Ser. A Math. Sci. 75 (1999), 58-60. MR1701526 (2000e:30037)
11. D. A. Herron, X. Liu, and D. Minda, Ring domains with separating circles or separating annuli, J. Anal. Math. 53 (1989), 233-252. MR1014988 (91i:30018)
12. T. Iwaniec and G. Martin, The Beltrami equation - In memory of Eugenio Beltrami (1835-1900), 100 years on, Memoires of the AMS, American Mathematical Society, to appear.
13. V. I. Kruglikov, The existence and uniqueness of mappings that are quasiconformal in the mean, Metric questions of the theory of functions and mappings, No. IV (Russian), Izdat. "Naukova Dumka", Kiev, 1973, pp. 123-147. MR0344462 (49:9201)
14. O. Lehto, Homeomorphisms with a given dilatation, Proceedings of the Fifteenth Scandinavian Congress (Oslo, 1968), Springer, 1970, pp. 58-73. MR0260997 (41:5617)
15. _, Remarks on generalized Beltrami equations and conformal mappings, Proceedings of the Romanian-Finnish Seminar on Teichmüller Spaces and Quasiconformal Mappings (Braşov, 1969), Publ. House of the Acad. of the Socialist Republic of Romania, Bucharest, 1971, pp. 203-214. MR0306489 (46:5615)
16. O. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, 2nd Ed., Springer-Verlag, 1973. MR0344463 (49:9202)
17. V. G. Maz'ja, Sobolev spaces, Springer-Verlag, Berlin, 1985, Translated from the Russian by T. O. Shaposhnikova. MR0817985 (87g:46056)
18. V. M. Miklyukov and G. D. Suvorov, The existence and uniqueness of quasiconformal mappings with unbounded characteristics (Russian), Studies in the theory of functions of a complex variable and its applications, Vidannja Inst. Mat. Akad. Nauk Ukraïn. RSR, Kiev, 1972, pp. 45-53. MR0338361 (49:3126)
19. I. N. Pesin, Mappings which are quasiconformal in the mean (Russian), Dokl. Akad. Nauk SSSR 187 (1969), 740-742, English translation in Soviet Math. Dokl. 10 (1969), 939-941. MR0249613 (40:2856)
20. I. N. Pesin, Mappings which are quasiconformal in the mean (Russian), Dokl. Akad. Nauk SSSR 187 (1969), 740-742, English translation in Soviet Math. Dokl. 10 (1969), 939-941. MR0249613 (40:2856)
21. E. Reich and H. Walczak, On the behavior of quasiconformal mappings at a point, Trans. Amer. Math. Soc. 117 (1965), 338-351. MR0176070 (31:345)
22. V. Ryazanov, U. Srebro, and E. Yakubov, BMO-quasiregular mappings, J. Anal. Math. 83 (2001), 1-20. MR1828484 (2002a:30034)
23. U. Srebro and E. Yakubov, μ-homeomorphisms, Lipa's legacy (New York, 1995) (Providence, RI), Amer. Math. Soc., Providence, RI, 1997, pp. 473-479. MR1477004 (99c:30043)
24. G. D. Suvorov, Families of plane topological mappings (Russian), Izdat. Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk, 1965. MR0199425 (33:7570)
25. P. Tukia, Compactness properties of μ-homeomorphisms, Ann. Acad. Sci. Fenn. Ser. A I Math. 16 (1991), 47-69. MR1127696 (93c:30029)