Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 591, 2006, Pages 49-74

  Astala, K ^a,b   Iwaniec, T ^a,c   Martin, G ^a,d  

^a University of Helsinki ^*

^b UNIVERSITY OF HELSINKI   (Finland)

^c SYRACUSE UNIVERSITY   (United States)

^d UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646703092     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/CRELLE.2006.014     Document Type: Article

References (24)

1. L. V. Ahlfors and A. Beurling, Conformal invariants and function theoretic null sets, Acta Math. 83 (1950), 101-129.
2. n, Vestnik Leningrad University 21 (1966), 5-10.
3. Amer. Math. Soc. Transl. (2) 68 (1968), 162-168.
4. K. Astala, Area distortion of quasiconformal mappings, Acta Math. 173 (1994), 37-60.
5. K. Astala, T. Iwaniec and G. J. Martin, Elliptic Differential Equations and Quasiconformal Mappings in the Plane, Monograph in preparation.
6. K. Astala, T. Iwaniec and E. Saksman, Beltrami Operators, Duke Math. J. 107 (2001), 27-56.
7. p-theory of Elliptic Equations, in preparation.
8. X. Cabré, On the Alexandroff-Bakelman-Pucci estimate and the reversed Hölder inequality for solutions of elliptic and parabolic equations, Comm. Pure Appl. Math. 48 (1995), 539-570.
9. L. A. Caffarelli and X. Cabré, Fully nonlinear elliptic equations, Amer. Math. Soc. Colloqu. Publ. 43 (1995).
10. ∞ = I, Ann. Acad. Sci. Fenn. Ser. A I Math. 13 (1988), 25-70.
11. D. Faraco, Milton's conjecture on the regularity of solutions to isotropic equations, Ann. Inst. H. Poincaré Anal. Non Lin. 20 (2003), 889-909.
12. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983.
13. V. M. Goldstein and S. K. Vodop'yanov, Quasiconformal mappings and spaces of functions with generalised first derivatives, Sb. Mat. Z. 17 (1976), 515-531.
14. α ℒ-integrability, J. London Math. Soc. (2) 67 (2003), 123-136.
15. T. Iwaniec, P. Koskela and J. Onninen, Mappings of finite distortion: monotonicity and continuity, Invent. Math. 144 (2001), 507-531.
16. T. Iwaniec and G. J. Martin, Geometric Function Theory and Nonlinear Analysis, Oxford University Press, 2001.
17. n, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 267-282.
18. T. Iwaniec and V. Šverák, On mappings with integrable dilatation, Proc. Amer. Math. Soc. 118 (1993), 181-188.
19. G. Moscariello, On the integrability of the Jacobian in Orlicz spaces, Math. Japonica 40 (1992), 323-329.
20. S. Müller, A surprising higher integrability property of mappings with positive determinant, Bull. Amer. Math. Soc. 21 (1989), 245-248.
21. S. Petermichl and A, Volberg, Heating of the Beurling operator: weakly quasiregular mappings are quasiregular, Duke Math. J. 112 (2002), 281-305.
22. C. Pucci, Limitazioni per soluzioni di equazioni ellittiche, Ann. Mat. Pura. Appl. (4) 74 (1966), 15-30.
23. C. Pucci, Operatori ellittici estremanti, Ann. Mat. Pura. Appl. (4) 72 (1966), 141-170.
24. N. S. Trudinger, New maximum principles for linear elliptic equations, preprint.