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A surprising higher integrability property of mappings with positive determinant


Author: Stefan Müller
Journal: Bull. Amer. Math. Soc. 21 (1989), 245-248
MSC (1985): Primary 49A22, 58C25; Secondary 26B35, 73C50
DOI: https://doi.org/10.1090/S0273-0979-1989-15818-7
MathSciNet review: 999618
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  • [B] J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337-403. MR 475169
  • J. M. Ball and F. Murat, 𝑊^{1,𝑝}-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), no. 3, 225–253. MR 759098, https://doi.org/10.1016/0022-1236(84)90041-7
  • Ronald J. DiPerna and Andrew J. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys. 108 (1987), no. 4, 667–689. MR 877643
  • [ET] I. Ekeland and R. Teman, Convex analysis and variational problems, North-Holland, Amsterdam, 1976.
  • [F] H. Federer, Geometric measure theory, Springer-Verlag, Berlin, Heidelberg, New York, 1969. MR 257325
  • P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 2, 109–145 (English, with French summary). MR 778970
  • P.-L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. I, Rev. Mat. Iberoamericana 1 (1985), no. 1, 145–201. MR 834360, https://doi.org/10.4171/RMI/6
  • [M] S. Müller, Higher integrability of determinants and weak compactness in L1, preprint.
  • [R] Y. G. Reshetnyak, Stability theorems for mappings with bounded excursion, Siberian Math. J. 9 (1968), 499-512.
  • [S1] E. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J., 1970. MR 290095
  • [S2] E. Stein, Note on the class LlogL, Studia Math. 32 (1969), 305-310. MR 247534
  • [Z] K. W. Zhang, Biting theorems for jacobians and their applications, preprint.

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DOI: https://doi.org/10.1090/S0273-0979-1989-15818-7

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