Regularity results for a class of quasiconvex functionals with nonstandard growth

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1. [AF1] E. Acerbi - N. Fusco, Semicontinuity problems in the Calculus of Variations, Arch. Rational Mech. Anal.86 (1984), 125-145. Zbl0565.49010MR751305
2. [AF2] E. Acerbi - N. Fusco, A regularity theorem for minimizers of quasiconvex integrals, Arch. Rational Mech. Anal.99 (1987), 261-281. Zbl0627.49007MR888453
3. [AF3] E. Acerbi - N. Fusco, Partial regularity under anisotropic (p, q) growth conditions, J. Differential Equations107 (1994), 46-67. Zbl0807.49010MR1260848
4. [AM1] E. Acerbi - G. Mingione, Regularity results for a class of functionals with nonstandard growth, Arch. Rational Mech. Anal.156 (2001), 121-140. Zbl0984.49020MR1814973
5. [AM2] E. Acerbi - G. Mingione, Regularity results for electrorheological fluids: the stationary case, to appear. Zbl1017.76098MR1905047
6. [A] Yu. A. Alkhutov, The Harnack inequality and the Hölder property of solutions of nonlinear elliptic equations with a nonstandard growth condition, Differential Equations33 (1997), 1653-1663. Zbl0949.35048MR1669915
7. [BF] M. Bildhauer - M. Fuch, Partial regularity for variational integrals with (s, μ, q)-growth, Calc. Var., to appear. Zbl1018.49026
8. [CFM] M. Carozza - N. Fusco - G. Mingione, Partial regularity of minimizers of quasiconvex integrals with subquadratic growth, Ann. Mat. Pura Appl.175 (1998), 141-164. Zbl0960.49025MR1748219
9. [CC] V. Chiadò Piat - A. Coscia, Hölder continuity of minimizers of functionals with variable growth exponent, Manuscripta Math.93 (1997), 283-299. Zbl0878.49010MR1457729
10. [CM] A. Coscia - G. Mingione, Hölder continuity of the gradient of p(x)-harmonic mappings, C. R. Acad. Sci. Paris328 (1999), 363-368. Zbl0920.49020MR1675954
11. [CFP] G. Cupini - N. Fusco - R. Petti, Hölder continuity of local minimizers, J. Math. Anal. Appl.235 (1999), 578-597. Zbl0949.49022MR1703712
12. [Ek] I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc.1 (1979), 443-474. Zbl0441.49011MR526967
13. [ELM] L. Esposito - F. Leonetti - G. Mingione, Higher integrability for minimizers of integralfunctionals with (p, q) growth, J. Differential Equations157 (1999), 414-438. Zbl0939.49021MR1713266
14. [EM] L. Esposito - G. Mingione, Partial regularity for minimizers of convex integrals with L log L-growth, NoDEA Nonlinear Differential Equations Appl.7 (1) (2000), 107-125 Zbl0954.49026MR1746116
15. [E] L. Evans, Quasiconvexity and partial regularity in the Calculus of Variations, Arch. Rational Mech. Anal.95 (1986), 227-252. Zbl0627.49006MR853966
16. [EG] L. Evans - R. Gariepy, Blow-up, compactness and partial regularity in the Calculus of Variations, Indiana Univ. Math. J.36 (1987), 361-371. Zbl0626.49007MR891780
17. [FZ] Fan Xiangling - Zhao Dun, A class of De Giorgi type and Hölder continuity, Nonlinear Anal. 36 (A) (1999), 295-318. Zbl0927.46022MR1688232
18. [FS] M. Fuchs - G. Seregin, A regularity theory for variational integrals with L log L-growth, Calc. Var. Partial Differential Equations6 (1998), 171-187. Zbl0929.49022MR1606481
19. [FH] N. Fusco - J. Hutchinson, C1,α partial regularity of functions minimizing quasiconvex integrals, Manuscripta Math. 54 (1985), 121-143. Zbl0587.49005
20. [Gia] M. Giaquinta, "Multiple integrals in Calculus of Variations and nonlinear elliptic sistems", Annals of Math. Studies105, Princeton Univ. Press, 1983. Zbl0516.49003MR717034
21. [Giu] E. Giusti, "Metodi Diretti nel Calcolo delle Variazioni ", UMI, Bologna, 1994. Zbl0942.49002MR1707291
22. [I] T. Iwaniec, The Gehring lemma, In: P.L. Duren and oth. (eds.) "Quasiconformal mappings and analysis: papers honoring F.W. Gehring", Ann. Arbour, MI, Springer Verlag, 1995, 181-204. Zbl0888.30017MR1488451
23. [M1] P. Marcellini, Regularity of minimizers of integrals of the Calculus of Variations with non standard growth conditions, Arch. Rational Mech. Anal.105 (1989), 267-284. Zbl0667.49032MR969900
24. [M2] P. Marcellini, Regularity and existence of solutions of elliptic equations with p, q-growth conditions, J. Differential Equations90 (1991), 1-30. Zbl0724.35043MR1094446
25. [M3] P. Marcellini, Regularity for elliptic equations with general growth conditions, J. Differential Equations105 (1993), 296-333. Zbl0812.35042MR1240398
26. [M4] P. Marcellini, Everywhere regularity for a class of elliptic systems without growth conditions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 23 (1996), 1-25. Zbl0922.35031MR1401415
27. [M5] P. Marcellini, Regularity for some scalar variational problems under general growth conditions, J. Optim. Theory Appl. 90 (1996), 161-181. Zbl0901.49030MR1397651
28. [RR] K.R. Rajagopal - M. Růžička, Mathematical modelling of electrorheological fluids, Cont. Mech. Therm.13 (1) (2001), 59-78. Zbl0971.76100
29. [R1] M Růžička, Flow of shear dependent electrorheological, fluids, C. R. Acad. Sci. Paris329 (1999), 393-398. Zbl0954.76097MR1710119
30. [R2] M Růžička, Electrorheological fluids: modeling and mathematical theory, Springer, Lecture Notes in Math. 1748 (2000). Zbl0962.76001MR1810360
31. [Z1] V.V. Zhikov, On Lavrentiev's phenomenon, Russian J. Math. Physics3 (1995), 249-269. Zbl0910.49020MR1350506
32. [Z2] V.V. Zhikov, On some variational problems, Russian J. Math. Physics5 (1997), 105-116. Zbl0917.49006MR1486765
33. [Z3] V.V. Zhikov, Meyers-type estimates for solving the non linear Stokes system, Differential Equations33 (1) (1997), 107-114. Zbl0911.35089MR1607245

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3. Alessandra Coscia, Domenico Mucci, Integral representation and Γ-convergence of variational integrals with -growth
4. Sabine Schemm, Partial regularity of minimizers of higher order integrals with (, )-growth
5. Michela Eleuteri, Hölder continuity results for a class of functionals with non-standard growth
6. Sabine Schemm, Partial regularity of minimizers of higher order integrals with (, )-growth
7. Giuseppe Mingione, Regularity of minima: an invitation to the Dark Side of the Calculus of Variations