Remarks on ${W}^{1,p}$-stability of the conformal set in higher dimensions
Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 6, pp. 691-705.
@article{AIHPC_1996__13_6_691_0,
author = {Yan, Baisheng},
title = {Remarks on $W^{1,p}$-stability of the conformal set in higher dimensions},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {691--705},
publisher = {Gauthier-Villars},
volume = {13},
number = {6},
year = {1996},
zbl = {00975970},
mrnumber = {1420494},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_1996__13_6_691_0/}
}
Yan, Baisheng. Remarks on $W^{1,p}$-stability of the conformal set in higher dimensions. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 6, pp. 691-705. http://archive.numdam.org/item/AIHPC_1996__13_6_691_0/

[1] E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal., Vol. 86, 1984, pp. 125-145. | MR 751305 | Zbl 0565.49010

[2] J.M. Ball, A version of the fundamental theorem for Young measures, in "Partial Differential Equations and Continuum Models of Phase Transitions," (M. Rascle, D. Serre and M. Slemrod eds.), Lecture Notes in Physics, Vol. 344, Springer-Verlag, Berlin, Heidelberg, New York, 1988. | MR 1036070 | Zbl 0991.49500

[3] J.M. Ball, Sets of gradients with no rank-one connections, J. math. pures et appl., Vol. 69, 1990, pp. 241-259. | MR 1070479 | Zbl 0644.49011

[4] J.M. Ball and F. Murat, W1,p-Quasiconvexity and variational problems for multiple integrals, J. Funct. Anal., Vol. 58, 1984, pp. 225-253. | MR 759098 | Zbl 0549.46019

[5] J.M. Ball and F. Murat, Remarks on Chacon's biting lemma, Proc. Amer. Math. Soc., Vol. 3, 1989, pp. 655-663. | MR 984807 | Zbl 0678.46023

[6] J.M. Ball and K. Zhang, Lower semicontinuity of multiple integrals and the Biting Lemma, Proc. Roy. Soc. Edinburgh, Vol. 114A, 1990, pp. 367-379. | MR 1055554 | Zbl 0716.49011

[7] K. Bhattacharya, N. Firoozye, R. James and R. Kohn, Restrictions on microstructure, Proc. Roy. Soc. Edin., A, Vol. 124, 1994, pp. 843-878. | MR 1303758 | Zbl 0808.73063

[8] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, Heidelberg, New York, 1989. | MR 990890 | Zbl 0703.49001

[9] L.C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS, Vol. 74, 1992.

[10] L.C. Evans and R.F. Gariepy, Some remarks on quasiconvexity and strong convergence, Proc. Roy. Soc. Edinburg, Ser. A, Vol. 106, 1987, pp. 53-61. | MR 899940 | Zbl 0628.49011

[11] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, 1983. | MR 717034 | Zbl 0516.49003

[12] T. Iwaniec, On Lp-integrability in PDE's and quasiregular mappings for large exponents, Ann. Acad. Sci. Fenn., Ser. A.I., Vol. 7, 1982, pp. 301-322. | MR 686647 | Zbl 0505.30011

[13] T. Iwaniec, p-Harmonic tensors and quasiregular mappings, Ann. Math., Vol. 136, 1992, pp. 589-624. | MR 1189867 | Zbl 0785.30009

[14] T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math., Vol. 170, 1993, pp. 29-81. | MR 1208562 | Zbl 0785.30008

[15] T. Iwaniec and C. Sbordone, Weak minima of variational integrals, J. rein angew. Math., Vol. 454, 1994, pp. 143-161. | MR 1288682 | Zbl 0802.35016

[16] D. Kinderlehrer, Remarks about equilibrium configurations of crystals, In Material Instabilities in Continuum Mechanics, (J. M. Ball ed.), Oxford University Press, 1988. | MR 970527 | Zbl 0850.73037

[17] D. Kinderlehrer and P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces, J. Geom. Anal., Vol. 4(1), 1994, pp. 59-90. | MR 1274138 | Zbl 0808.46046

[18] C.B. Jr. Morrey, Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, Heidelberg, New York, 1966. | MR 202511 | Zbl 0142.38701

[19] S. Müller and V. Šverák, Attainment results for the two well problem by convex integration, 1993, preprint.

[20] S. Muller, V. Šverák and B. Yan, Sharp stability results for almost conformal maps in even dimensions, 1995, preprint.

[21] Yu.G. Reshetnyak, Space Mappings with Bounded Distortion, Transl. Math. Mono., AMS, Vol. 73, 1989. | MR 994644 | Zbl 0667.30018

[22] S. Rickman, Quasiregular Mappings, Springer-Verlag, Berlin, Heidelberg, New York, 1993. | MR 1238941 | Zbl 0816.30017

[23] V. Šverák, On regularity for the Monge-Ampère equation without convexity assumptions, Preprint, 1992.

[24] V. Šverák, On Tartar's conjecture, Ann. Inst. H. Poincaré, Analyse non linéaire, Vol. 10(4), 1993, pp. 405-412. | Numdam | MR 1246459 | Zbl 0820.35022

[25] L. Tartar, The compensated compactness method applied to systems of conservation laws, in Systems of Nonlinear Partial Differential Equations, (J. M. Ball ed.), NATO ASI Series, Vol. CIII, D. Reidel, 1983. | MR 725524 | Zbl 0536.35003

[26] B. Yan, On quasiconvex hulls of sets of matrices and strong convergence of certain minimizing sequences, Preprint, 1993.

[27] B. Yan, On rank-one convex and polyconvex conformal energy functions with slow growth, 1994, preprint. | MR 1453286

[28] K. Zhang, Biting theorems for Jacobians and their applications, Ann. Inst. H. Poincaré, Analyse non linéaire, Vol. 7, 1990, pp. 345-365. | Numdam | MR 1067780 | Zbl 0717.49012

[29] K. Zhang, A construction of quasiconvex functions with linear growth at infinity, Ann. Scuola Norm. Sup. Pisa, Vol. 19(3), 1992, pp. 313-326. | Numdam | MR 1205403 | Zbl 0778.49015

[30] K. Zhang, Monge-Ampère equations and multiwell problems, 1993, preprint.