References
Acerbi, E., & Fusco, N., Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984), 125–145.
Ball, J. M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337–403.
Ball, J. M., & Murat, F., W 1,p-quasi-convexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), 225–253.
Bojarski, B., & Iwaniec, T., Analytical foundations of the theory of quasiconformal mappings in R n, Ann. Acad. Sci. Fenn. Ser. A.I. 8 (1983), 257–324.
Buttazzo, G., Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman (1990).
Carbone, L., & De Arcangelis, R., Further results on Γ-convergence and lower Semicontinuity of integral functionals depending on vector-valued functions, Ric. di Mat. 39 (1990), 99–129.
Coifman, R. R., Lions, P. L., Meyer, Y., & Semmes, S., Compacité par compensation et espaces de Hardy, Comptes Rendus Acad. Sci. Paris 309 (1989), 945–949.
Dacorogna, B., Direct Methods in the Calculus of Variations, Springer-Verlag (1990).
Dacorogna, B., & Marcellini, P., Semicontinuité pour des integrandes polyconvexes sans continuité des determinants, Comptes Rendus Acad. Sci. Paris 311, ser. I (1990), 393–396.
Dacorogna, B., & Murat, F., On the optimality of certain Sobolev exponents for the weak continuity of determinants, preprint (1991).
De Giorgi, E., Teoremi di Semicontinuitá nel Calcolo delle Variazioni, I.N.D.A.M. Roma (1968–1969).
Donaldson, T. K., & Trudinger, N. S., Orlicz-Sobolev Spaces and Imbedding Theorems, J. Funct. Anal. 8 (1971), 52–75.
Giaquinta, M., Multiple integrals in the Calculus of Variations and nonlinear elliptic systems, Princeton Univ. Press (1983).
Gehring, F. W., The L p-integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265–277.
Giaquinta, M., Modica, G., & Souček, J., Cartesian currents, weak diffeomorphism and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 106 (1989), 97–159.
Iwaniec, T., p-Harmonic tensors and quasiregular mappings, to appear in Annals of Mathematics.
Iwaniec, T., L p-theory of quasiregular mappings, Collection of Surveys on Quasiconformal Space Mappings, to appear in Lecture Notes in Mathematics (1992).
Iwaniec, T., On Cauchy-Riemann derivatives in several real variables, Springer Lecture Notes in Math. 1039 (1983), 220–244.
Iwaniec, T., & Kosecki, R., Sharp estimates for complex potentials and quasiconformal mappings, preprint.
Iwaniec, T. & Lutoborski, A., Integral estimates for null Lagrangians, in preparation.
Iwaniec, T., & Sbordone, C., Weak minima of variational integrals, in preparation.
Marcellini, P., On the definition and the lower semicontinuity of certain quasi convex integrals, Ann. Inst. Poincaré 35 (1986), 391–409.
Müller, S., Det ▽u = det ▽u, Comptes Rendus Acad. Sci. Paris 311 (1990), 13–17.
Müller, S., Higher integrability of determinants and weak convergence in L 1, J. reine angew. Math. 412 (1990), 20–34.
Reshetnyak, Y. G., On the stability of conformal mappings in multidimensional spaces, Siber. Math. J. 8 (1967), 65–85.
Rao, M. M. & Ren, Z. D., Theory of Orlicz Spaces, M. Dekker (1991).
Stein, E.M., Note on the class L log L, Studia Math. 32 (1969), 305–310.
Tartar, L., Hardy's spaces and applications, preprint (1989).
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Communicated by J. M. Ball
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Iwaniec, T., Sbordone, C. On the integrability of the Jacobian under minimal hypotheses. Arch. Rational Mech. Anal. 119, 129–143 (1992). https://doi.org/10.1007/BF00375119
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DOI: https://doi.org/10.1007/BF00375119