Free access
Issue
ESAIM: COCV
Volume 14, Number 2, April-June 2008
Page(s) 211 - 232
DOI http://dx.doi.org/10.1051/cocv:2007049
Published online 20 March 2008
  1. E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal 86 (1984) 125–145. [CrossRef] [MathSciNet]
  2. E. Acerbi and N. Fusco, A regularity theorem for minimizers of quasiconvex integrals. Arch. Rational Mech. Anal 99 (1987) 261–281. [CrossRef] [MathSciNet]
  3. E. Acerbi and N. Fusco, An approximation lemma for Formula functions, in Material instabilities in continuum mechanics (Edinburgh, 1985–1986), Oxford Sci. Publ., Oxford Univ. Press, New York (1988) 1–5.
  4. L. Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Nonlinear Anal 19 (1992) 581–597. [CrossRef] [MathSciNet]
  5. M.E. Bogovskiĭ, Solutions of some problems of vector analysis, associated with the operators Formula and Formula , in Theory of cubature formulas and the application of functional analysis to problems of mathematical physics (Russian) 149, Akad. Nauk SSSR Sibirsk. Otdel. Inst. Mat., Novosibirsk (1980) 5–40.
  6. D. Cruz-Uribe, A. Fiorenza and C.J. Neugebauer, The maximal function on variable Formula spaces. Ann. Acad. Sci. Fenn. Math 28 (2003) 223–238. [MathSciNet]
  7. D. Cruz-Uribe, A. Fiorenza, J.M. Martell and C. Peréz, The boundedness of classical operators on variable Formula spaces. Ann. Acad. Sci. Fenn. Math 31 (2006) 239–264. [MathSciNet]
  8. G. Dal Maso and F. Murat, Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems. Nonlinear Anal 31 (1998) 405–412. [CrossRef] [MathSciNet]
  9. L. Diening, Maximal function on generalized Lebesgue spaces Formula . Math. Inequal. Appl 7 (2004) 245–253. [MathSciNet]
  10. L. Diening, Riesz potential and Sobolev embeddings of generalized Lebesgue and Sobolev spaces Formula and Formula . Math. Nachrichten 268 (2004) 31–43. [CrossRef]
  11. L. Diening and P. Hästö, Variable exponent trace spaces. Studia Math (2007) to appear.
  12. L. Diening and M. Růžička, Calderón-Zygmund operators on generalized Lebesgue spaces Formula and problems related to fluid dynamics J. Reine Angew. Math 563 (2003) 197–220.
  13. G. Dolzmann, N. Hungerbühler and S. Müller, Uniqueness and maximal regularity for nonlinear elliptic systems of n-Laplace type with measure valued right hand side. J. Reine Angew. Math 520 (2000) 1–35. [CrossRef] [MathSciNet]
  14. F. Duzaar and G. Mingione, The p-harmonic approximation and the regularity of p-harmonic maps. Calc. Var. Partial Diff. Eq 20 (2004) 235–256. [CrossRef]
  15. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. CRC Press, Boca Raton, FL, (1992).
  16. X. Fan and D. Zhao, On the spaces Formula and Formula . J. Math. Anal. Appl 263 (2001) 424–446. [CrossRef] [MathSciNet]
  17. H. Federer, Geometric Measure Theory Band 153 of Die Grundlehren der mathematischen Wissenschaften. Springer-Verlag, Berlin-Heidelberg-New York (1969).
  18. J. Frehse, J. Málek, and M. Steinhauer, On analysis of steady flows of fluids with shear-dependent viscosity based on the Lipschitz truncation method. SIAM J. Math. Anal 34 (2003) 1064–1083 (electronic). [CrossRef] [MathSciNet]
  19. M. Giaquinta, G. Modica and J. Souček, Cartesian currents in the calculus of variations. I, vol. 37 of Ergebnisse der Mathematik. 3. Folge. A Series of Modern Surveys in Mathematics. Springer-Verlag, Berlin (1998).
  20. L. Greco, T. Iwaniec and C. Sbordone, Variational integrals of nearly linear growth. Diff. Int. Eq 10 (1997) 687–716.
  21. A. Huber, Die Divergenzgleichung in gewichteten Räumen und Flüssigkeiten mit Formula -Struktur. Ph.D. thesis, University of Freiburg, Germany (2005).
  22. O. Kováčik and J. Rákosník, On spaces Formula and Formula . Czechoslovak Math. J 41 (1991) 592–618. [MathSciNet]
  23. R. Landes, Quasimonotone versus pseudomonotone. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996) 705–717. [MathSciNet]
  24. A. Lerner, Some remarks on the Hardy-Littlewood maximal function on variable Lp spaces. Math. Z 251 (2005) 509–521. [CrossRef] [MathSciNet]
  25. J. Málek and K.R. Rajagopal, Mathematical issues concerning the Navier-Stokes equations and some of its generalizations, in Evolutionary Equations, volume 2 of Handbook of differential equations, C. Dafermos and E. Feireisl Eds., Elsevier B. V. (2005) 371–459.
  26. J. Malý and W.P. Ziemer, Fine regularity of solutions of elliptic partial differential equations. American Mathematical Society, Providence, RI (1997).
  27. S. Müller, A sharp version of Zhang's theorem on truncating sequences of gradients. Trans. Amer. Math. Soc 351 (1999) 4585–4597. [CrossRef] [MathSciNet]
  28. A. Nekvinda, Hardy-Littlewood maximal operator on Formula . Math. Inequal. Appl 7 (2004) 255–265. [MathSciNet]
  29. P. Pedregal, Parametrized measures and variational principles. Progress in Nonlinear Diff. Eq. Applications, Birkhäuser Verlag, Basel (1997).
  30. L. Pick and M. Růžička, An example of a space Formula on which the Hardy-Littlewood maximal operator is not bounded. Expo. Math 19 (2001) 369–371. [CrossRef] [MathSciNet]
  31. K.R. Rajagopal and M. Růžička, On the modeling of electrorheological materials Mech. Res. Commun 23 (1996) 401–407.
  32. K.R. Rajagopal and M. Růžička, Mathematical modeling of electrorheological materials. Cont. Mech. Thermodyn 13 (2001) 59–78. [CrossRef]
  33. M. Růžička, Electrorheological fluids: modeling and mathematical theory, Lect. Notes Math. 1748. Springer-Verlag, Berlin (2000).
  34. K. Zhang, On the Dirichlet problem for a class of quasilinear elliptic systems of partial differential equations in divergence form, in Partial differential equations (Tianjin, 1986), Lect. Notes Math 1306 (1988) 262–277.
  35. K. Zhang, Biting theorems for Jacobians and their applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 345–365.
  36. K. Zhang, A construction of quasiconvex functions with linear growth at infinity. Ann. Scuola Norm. Sup. Pisa Cl. Sci 19 (1992) 313–326. [MathSciNet]
  37. K. Zhang, Remarks on perturbated systems with critical growth. Nonlinear Anal 18 (1992) 1167–1179. [CrossRef] [MathSciNet]
  38. W.P. Ziemer. Weakly differentiable functions. Sobolev spaces and functions of bounded variation, Graduate Texts in Mathematics 120. Springer-Verlag, Berlin (1989) 308.