Milton's conjecture on the regularity of solutions to isotropic equations
Faraco, Daniel
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 889-909 / Harvested from Numdam
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@article{AIHPC_2003__20_5_889_0,
     author = {Faraco, Daniel},
     title = {Milton's conjecture on the regularity of solutions to isotropic equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {889-909},
     doi = {10.1016/S0294-1449(03)00014-3},
     mrnumber = {1995506},
     zbl = {1029.30012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_5_889_0}
}

Faraco, Daniel. Milton's conjecture on the regularity of solutions to isotropic equations. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 889-909. doi : 10.1016/S0294-1449(03)00014-3. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_5_889_0/

[1] Ahlfors L.V., Lectures on Quasiconformal Mappings, Van Nostrand, Princenton, 1966. | MR 200442 | Zbl 0138.06002

[2] Astala K., Area distortion of quasiconformal mappings, Acta Math. 173 (1994) 37-60. | MR 1294669 | Zbl 0815.30015

[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. | MR 1815249 | Zbl 1009.30015

[5] K. Astala, D. Faraco, Quasiregular mappings and Young measures, Proc. Roy. Soc. Edinburgh Sect. A, to appear. | MR 1938712 | Zbl 1016.30016

[6] K. Astala, V. Nesi, Composites and quasiconformal mappings: New optimal bounds in two dimensions, Calc. Var. Partial Differential Equations, to appear. | MR 2020365 | Zbl 1106.74052

[7] Braides A., Defranceschi A., Homogenization of Multiple Integrals, Oxford Lecture Series in Mathematics and its Applications, 12, Clarendon Press/Oxford University Press, New York, 1998. | MR 1684713 | Zbl 0911.49010

[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). | MR 106324

[9] Dacorogna B., Marcellini P., Implicit Partial Differential Equations, Progress in Nonlinear Differential Equations and Their Applications, 37, Birkhäuser, 1999. | MR 1702252 | Zbl 0938.35002

[10] Erëmenko A., Hamilton D.H., On the area distortion by quasiconformal mappings, Proc. Amer. Math. Soc. 123 (9) (1995) 2793-2797. | MR 1283548 | Zbl 0841.30013

[11] D. Faraco, Tartar Conjecture and Beltrami Operators, Preprint at the University of Helsinki, 2002. | MR 2043398

[12] Iwaniec T., Sbordone C., Quasiharmonic fields, Ann. Inst. H. Poincaré Anal. Non Linaire 18 (5) (2001) 519-572. | Numdam | MR 1849688 | Zbl 1068.30011

[13] B. Kirheim, Geometry and rigidity of microstructures, Habilitation Thesis, Leipzig, 2001. | Zbl 01794210

[14] Koskela P., The degree of regularity of a quasiconformal mapping, Proc. Amer. Math. Soc. 122 (3) (1994) 769-772. | MR 1204381 | Zbl 0814.30015

[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. | MR 1432370 | Zbl 0869.35019

[16] Marino A., Spagnolo S., Un tipo di approssimazione dell'operatore ∑1nijDi(aij(x)Dj) con operatori ∑1njDj(β(x)Dj), Ann. Scuola Norm. Sup. Pisa (3) 23 (1969) 657-673, (Italian). | Numdam | Zbl 0187.35305

[17] Meyers N.G., An Lp estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa (3) 17 (1963) 189-206. | Numdam | MR 159110 | Zbl 0127.31904

[18] Milton G., Modelling the properties of composites by laminates, in: Homogenization and Effective Moduli of Materials and Media, IMA Volumes in Mathematics and its Applications, 1, Springer-Verlag, New York, 1986. | MR 859415 | Zbl 0631.73011

[19] Morrey C.B., On the solution of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938) 126-166. | JFM 64.0460.02 | MR 1501936

[20] Müller S., Šverák V., Unexpected solutions of first and second order partial differential equations, Doc. Math. J. DMV ICM (1998) 691-702. | MR 1648117 | Zbl 0896.35029

[21] S. Müller, V. Šverák, Convex integrations with constrains and applications to phase transitions and partial differtential equations, MPI MIS, Preprint 98, 1999. | MR 1728376

[22] Pedregal P., Laminates and microstructure, Eur. J. Appl. Math. 4 (1993) 121-149. | MR 1228114 | Zbl 0779.73050

[23] Pedregal P., Parametrized Measures and Variational Principles, Birkhäuser, 1997. | MR 1452107 | Zbl 0879.49017

[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. | Numdam | MR 361422 | Zbl 0237.35028