Mappings of finite distortion: Monotonicity and continuity

Inventiones Mathematicae

Volumn 144, Issue 3, 2001, Pages 507-531

  Iwaniec, Tadeusz ^a   Koskela, Pekka ^b   Onninen, Jani ^b  

^a SYRACUSE UNIVERSITY   (United States)

^b UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035638729     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220100130     Document Type: Article

References (32)

1. Astala, K., Iwaniec, T., Koskela, P., Martin, G. (2000). Mappings of BMO-bounded distortion. Math. Ann. 317, 4, 703-726
2. Ball, J. (1978). Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63, 337-403
3. Ball, J. (1981). Global invertibility of Sobolev functions and the interpenetration of matter. Proc. Roy. Soc. Edinburgh Sect. A 88, 3-4, 315-328
4. Brakalova, M.A., Jenkins, J.A. (1998). On solutions of the Beltrami equation. J. Anal. Math. 76, 67-92
5. ∞ = 1. Ann Acad. Sci. Fenn. Ser. A I, Math. 13, 1, 25-70
6. Gehring, F.W. (1962). Rings and quasiconformal mappings in space. Trans. Amer. Math. Soc. 103, 353-393
7. Gehring, F.W., Iwaniec, T. (1999). The limit of mappings with finite distortion. Ann. Acad. Sci. Fenn. Math. 24, 1, 253-264
8. Gol'dstein, V.M., Vodop'yanov, S.K. (1976). Quasiconformal mappings and spaces of functions with generalized first derivatives. Sibirsk. Mat. Z. 17, 515-531
9. Greco, L. (1993). A remark on the equality det D f = Det D f. Differential Integral Equations 6, 5, 1089-1100
10. Greco, L. (1998). Sharp integrability of nonnegative Jacobians. Rend. Mat. Appl. (7) 18, 3, 585-600
11. Greco, L. Iwaniec, T., Moscariello, G. (1995). Limits of the improved integrability of the volume forms. Indiana Univ. Math. J. 44, 2, 305-339
12. Hajłasz, P. (1995). A note on weak approximation of minors. Ann. Inst. H. Poincare Anal. Non Linéaire 12, 4, 415-424
13. Heinonen, J., Koskela, P. (1993). Sobolev mappings with integrable dilatations. Arch. Rational Mech. Anal. 125, 1, 81-97
14. Iwaniec, T. (1999). Nonlinear Differential Forms, Lectures at the International Summer School in Jyväskylä, 1998, Editor: P. Mattila University of Jyväskylä, Department of Mathematics Report 80, pp 1-207
15. Iwaniec, T., Koskela, P., Martin, G. Mappings of BMO-distortion and Beltrami type operators. Preprint
16. Iwaniec, T., Lutoborski, A. (1993). Integral estimates for null Lagrangians. Arch. Rational Mech. Anal. 125, 1, 25-79
17. Iwaniec, T., Martin, G. The Beltrami Equation. To appear in Mem. Amer. Math. Soc.
18. Iwaniec, T., Sbordone, C. (1992). On the integrability of the Jacobian under minimal hypotheses. Arch. Rational Mech. Anal. 119, 2, 129-143
19. Iwaniec, T., Šveràk, V. (1993). On mappings with integrable dilatation. Proc. Amer. Math. Soc. 118, 181-188
20. Lebesgue, H. (1907). Sur le problème de Dirichlet. Rend. Circ. Palermo 27, 371-402
21. Manfredi, J. (1994). Weakly Monotone Functions. J. Geom. Anal. 3, 393-402
22. Manfredi, J., Villamor, E. (1995). Mappings with integrable dilatation in higher dimensions. Bull. Amer. Math. Soc. (N.S.) 32, 2, 235-240
23. Manfredi, J., Villamor, E. (1998). An extension of Reshetnyak's theorem. Indiana Univ. Math. J. 47, 3, 1131-1145
24. Migliaccio, L., Moscariello, G. (1997). Mappings with unbounded dilatation. Preprint no. 3. Università di Salerno
25. Müller, S., Qi, T., Yan, B.S. (1994). On a new class of elastic deformations not allowing for cavitation. Ann. Inst. H. Poincaré Anal. Non Linéaire 11, 2, 217-243
26. Potemkin, V., Ryazanov, V (1998). On the noncompactness of David classes. Ann. Acad. Sci. Fenn. Math. 23, 191-204
27. Reshetnyak, Yu.G. (1966). Bounds on moduli of continuity for certain mappings. (Russian). Sibirsk. Mat. Sh. 7, 1106-1114
28. Reshetnyak, Yu.G. (1989). Space mappings with bounded distortion. Trans. Math. Monographs Amer. Math. Soc. 73
29. Ryazanov, V., Srebro, U., Yakubov, E. (1999). On the theory of BMO-quasiregular mappings. (Russian) Dokl. Akad. Nauk 369, 1, 13-15
30. Šveràk, V. (1988). Regularity properties of deformations with finite energy. Arch. Rational Mech. Anal. 100, 2, 105-127
31. Tukia, P. (1991). Compactness properties of μ-homeomorphisms. Ann. Acad. Sci. Fenn. Ser. A I. Math. 16, 47-69
32. Vodop'yanov, S.K. (1999). Mappings with bounded distortion and with finite distortion on Carnot groups. Siberian Math. J. 33, 4, 764-804