Archive for Rational Mechanics and Analysis

, Volume 119, Issue 2, pp 129–143 | Cite as

On the integrability of the Jacobian under minimal hypotheses

  • Tadeusz Iwaniec
  • Carlo Sbordone


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AF]
    Acerbi, E., & Fusco, N., Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984), 125–145.Google Scholar
  2. [B]
    Ball, J. M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337–403.Google Scholar
  3. [BM]
    Ball, J. M., & Murat, F., W 1,p-quasi-convexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), 225–253.Google Scholar
  4. [BI]
    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.Google Scholar
  5. [BU]
    Buttazzo, G., Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman (1990).Google Scholar
  6. [CD]
    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.Google Scholar
  7. [CLMS]
    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.Google Scholar
  8. [D]
    Dacorogna, B., Direct Methods in the Calculus of Variations, Springer-Verlag (1990).Google Scholar
  9. [DM]
    Dacorogna, B., & Marcellini, P., Semicontinuité pour des integrandes polyconvexes sans continuité des determinants, Comptes Rendus Acad. Sci. Paris 311, ser. I (1990), 393–396.Google Scholar
  10. [DMU]
    Dacorogna, B., & Murat, F., On the optimality of certain Sobolev exponents for the weak continuity of determinants, preprint (1991).Google Scholar
  11. [DG]
    De Giorgi, E., Teoremi di Semicontinuitá nel Calcolo delle Variazioni, I.N.D.A.M. Roma (1968–1969).Google Scholar
  12. [DT]
    Donaldson, T. K., & Trudinger, N. S., Orlicz-Sobolev Spaces and Imbedding Theorems, J. Funct. Anal. 8 (1971), 52–75.Google Scholar
  13. [G]
    Giaquinta, M., Multiple integrals in the Calculus of Variations and nonlinear elliptic systems, Princeton Univ. Press (1983).Google Scholar
  14. [GE]
    Gehring, F. W., The L p-integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265–277.Google Scholar
  15. [GMS]
    Giaquinta, M., Modica, G., & Souček, J., Cartesian currents, weak diffeomorphism and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 106 (1989), 97–159.Google Scholar
  16. [I1]
    Iwaniec, T., p-Harmonic tensors and quasiregular mappings, to appear in Annals of Mathematics.Google Scholar
  17. [I2]
    Iwaniec, T., L p-theory of quasiregular mappings, Collection of Surveys on Quasiconformal Space Mappings, to appear in Lecture Notes in Mathematics (1992).Google Scholar
  18. [I3]
    Iwaniec, T., On Cauchy-Riemann derivatives in several real variables, Springer Lecture Notes in Math. 1039 (1983), 220–244.Google Scholar
  19. [IK]
    Iwaniec, T., & Kosecki, R., Sharp estimates for complex potentials and quasiconformal mappings, preprint.Google Scholar
  20. [IL]
    Iwaniec, T. & Lutoborski, A., Integral estimates for null Lagrangians, in preparation.Google Scholar
  21. [IS]
    Iwaniec, T., & Sbordone, C., Weak minima of variational integrals, in preparation.Google Scholar
  22. [M]
    Marcellini, P., On the definition and the lower semicontinuity of certain quasi convex integrals, Ann. Inst. Poincaré 35 (1986), 391–409.Google Scholar
  23. [MU1]
    Müller, S., Det ▽u = det ▽u, Comptes Rendus Acad. Sci. Paris 311 (1990), 13–17.Google Scholar
  24. [MU2]
    Müller, S., Higher integrability of determinants and weak convergence in L 1, J. reine angew. Math. 412 (1990), 20–34.Google Scholar
  25. [R]
    Reshetnyak, Y. G., On the stability of conformal mappings in multidimensional spaces, Siber. Math. J. 8 (1967), 65–85.Google Scholar
  26. [RR]
    Rao, M. M. & Ren, Z. D., Theory of Orlicz Spaces, M. Dekker (1991).Google Scholar
  27. [S]
    Stein, E.M., Note on the class L log L, Studia Math. 32 (1969), 305–310.Google Scholar
  28. [T]
    Tartar, L., Hardy's spaces and applications, preprint (1989).Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Tadeusz Iwaniec
    • 1
    • 2
  • Carlo Sbordone
    • 1
    • 2
  1. 1.Dept. of MathematicsSyracuse UniversitySyracuse
  2. 2.Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Monte S. AngeloNapoli

Personalised recommendations