Milton's conjecture on the regularity of solutions to isotropic equations

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 20, Issue 5, 2003, Pages 889-909

  Faraco, Daniel ^a  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; ELECTRIC CONDUCTIVITY; INTEGRATION; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; SET THEORY; THEOREM PROVING;

BELTRAMI OPERATORS; ISOTROPIC EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0346093786     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(03)00014-3     Document Type: Article

References (24)

1. Ahlfors L.V. Lectures on Quasiconformal Mappings. 1966;Van Nostrand, Princenton.
2. Astala K. Area distortion of quasiconformal mappings. Acta Math. 173:1994;37-60.
3. K. Astala, In preparation.
4. Astala K., Iwaniec T., Saksman E. Beltrami operators in the plane. Duke Math. J. 107:(1):2001;27-56.
5. K. Astala, D. Faraco, Quasiregular mappings and Young measures, Proc. Roy. Soc. Edinburgh Sect. A, to appear.
6. K. Astala, V. Nesi, Composites and quasiconformal mappings: New optimal bounds in two dimensions, Calc. Var. Partial Differential Equations, to appear.
7. Braides A., Defranceschi A. Homogenization of Multiple Integrals. Oxford Lecture Series in Mathematics and its Applications. 12:1998;Clarendon Press/Oxford University Press, New York.
8. Bojarski B.V. Generalized solutions of a system of differential equations of first order and of elliptic type with discontinuous coefficients. Mat. Sb. NS. 43:(85):1957;451-503. (Russian).
9. Dacorogna B., Marcellini P. Implicit Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications. 37:1999;Birkhäuser.
10. Erëmenko A., Hamilton D.H. On the area distortion by quasiconformal mappings. Proc. Amer. Math. Soc. 123:(9):1995;2793-2797.
11. D. Faraco, Tartar Conjecture and Beltrami Operators, Preprint at the University of Helsinki, 2002.
12. Iwaniec T., Sbordone C. Quasiharmonic fields. Ann. Inst. H. Poincaré Anal. Non Linaire. 18:(5):2001;519-572.
13. B. Kirheim, Geometry and rigidity of microstructures, Habilitation Thesis, Leipzig, 2001.
14. Koskela P. The degree of regularity of a quasiconformal mapping. Proc. Amer. Math. Soc. 122:(3):1994;769-772.
15. Leonetti F., Nesi V. Quasiconformal solutions to certain first order systems and the proof of a conjecture of G.W. Milton. J. Math. Pures. Appl. (9). 76:1997;109-124.
16. j) . Ann. Scuola Norm. Sup. Pisa (3). 23:1969;657-673. (Italian).
17. p estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa (3). 17:1963;189-206.
18. Milton G. Modelling the properties of composites by laminates. Homogenization and Effective Moduli of Materials and Media. Ericksen, Kiderleher, Kohn, Lions. IMA Volumes in Mathematics and its Applications. 1:1986;Springer-Verlag, New York.
19. Morrey C.B. On the solution of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc. 43:1938;126-166.
20. Müller S., Šverák V. Unexpected solutions of first and second order partial differential equations. Doc. Math. J. DMV ICM:1998;691-702.
21. S. Müller, V. Šverák, Convex integrations with constrains and applications to phase transitions and partial differtential equations, MPI MIS, Preprint 98, 1999.
22. Pedregal P. Laminates and microstructure. Eur. J. Appl. Math. 4:1993;121-149.
23. Pedregal P. Parametrized Measures and Variational Principles. 1997;Birkhäuser.
24. Piccinini L.C., Spagnolo S. On the Hölder continuity of solutions of second order elliptic equations in two variables. Ann. Scuola Norm. Sup. Pisa (3). 26:1972;391-402.