Milton's conjecture on the regularity of solutions to isotropic equations
Annales de l'I.H.P. Analyse non linéaire (2003)
- Volume: 20, Issue: 5, page 889-909
- ISSN: 0294-1449
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topFaraco, Daniel. "Milton's conjecture on the regularity of solutions to isotropic equations." Annales de l'I.H.P. Analyse non linéaire 20.5 (2003): 889-909. <http://eudml.org/doc/78601>.
@article{Faraco2003,
author = {Faraco, Daniel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {isotropic equations},
language = {eng},
number = {5},
pages = {889-909},
publisher = {Elsevier},
title = {Milton's conjecture on the regularity of solutions to isotropic equations},
url = {http://eudml.org/doc/78601},
volume = {20},
year = {2003},
}
TY - JOUR
AU - Faraco, Daniel
TI - Milton's conjecture on the regularity of solutions to isotropic equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 5
SP - 889
EP - 909
LA - eng
KW - isotropic equations
UR - http://eudml.org/doc/78601
ER -
References
top- [1] Ahlfors L.V., Lectures on Quasiconformal Mappings, Van Nostrand, Princenton, 1966. Zbl0138.06002MR200442
- [2] Astala K., Area distortion of quasiconformal mappings, Acta Math.173 (1994) 37-60. Zbl0815.30015MR1294669
- [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. Zbl1009.30015MR1815249
- [5] K. Astala, D. Faraco, Quasiregular mappings and Young measures, Proc. Roy. Soc. Edinburgh Sect. A, to appear. Zbl1016.30016MR1938712
- [6] K. Astala, V. Nesi, Composites and quasiconformal mappings: New optimal bounds in two dimensions, Calc. Var. Partial Differential Equations, to appear. Zbl1106.74052MR2020365
- [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. Zbl0911.49010MR1684713
- [8] Bojarski B.V., Generalized solutions of a system of differential equations of first order and of elliptic type with discontinuous coefficients, Mat. Sb. NS43 (85) (1957) 451-503, (Russian). MR106324
- [9] Dacorogna B., Marcellini P., Implicit Partial Differential Equations, Progress in Nonlinear Differential Equations and Their Applications, 37, Birkhäuser, 1999. Zbl0938.35002MR1702252
- [10] Erëmenko A., Hamilton D.H., On the area distortion by quasiconformal mappings, Proc. Amer. Math. Soc.123 (9) (1995) 2793-2797. Zbl0841.30013MR1283548
- [11] D. Faraco, Tartar Conjecture and Beltrami Operators, Preprint at the University of Helsinki, 2002. MR2043398
- [12] Iwaniec T., Sbordone C., Quasiharmonic fields, Ann. Inst. H. Poincaré Anal. Non Linaire18 (5) (2001) 519-572. Zbl1068.30011MR1849688
- [13] B. Kirheim, Geometry and rigidity of microstructures, Habilitation Thesis, Leipzig, 2001. Zbl1140.74303
- [14] Koskela P., The degree of regularity of a quasiconformal mapping, Proc. Amer. Math. Soc.122 (3) (1994) 769-772. Zbl0814.30015MR1204381
- [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. Zbl0869.35019MR1432370
- [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). Zbl0187.35305
- [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. Zbl0127.31904MR159110
- [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. Zbl0631.73011MR859415
- [19] Morrey C.B., On the solution of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc.43 (1938) 126-166. Zbl0018.40501MR1501936JFM64.0460.02
- [20] Müller S., Šverák V., Unexpected solutions of first and second order partial differential equations, Doc. Math. J. DMVICM (1998) 691-702. Zbl0896.35029MR1648117
- [21] S. Müller, V. Šverák, Convex integrations with constrains and applications to phase transitions and partial differtential equations, MPI MIS, Preprint 98, 1999. MR1728376
- [22] Pedregal P., Laminates and microstructure, Eur. J. Appl. Math.4 (1993) 121-149. Zbl0779.73050MR1228114
- [23] Pedregal P., Parametrized Measures and Variational Principles, Birkhäuser, 1997. Zbl0879.49017MR1452107
- [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. Zbl0237.35028MR361422
Citations in EuDML Documents
top- Robert Lipton, Tadele Mengesha, Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
- Robert Lipton, Tadele Mengesha, Representation formulas for norms of weakly convergent sequences of gradient fields in homogenization
- Kari Astala, Daniel Faraco, László Székelyhidi Jr., Convex integration and the theory of elliptic equations
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