Regularity results for a class of quasiconvex functionals with nonstandard growth
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 30 (2001) no. 2, pp. 311-339.
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author = {Acerbi, Emilio and Mingione, Giuseppe},
title = {Regularity results for a class of quasiconvex functionals with nonstandard growth},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Acerbi, Emilio; Mingione, Giuseppe. Regularity results for a class of quasiconvex functionals with nonstandard growth. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 30 (2001) no. 2, pp. 311-339. http://www.numdam.org/item/ASNSP_2001_4_30_2_311_0/

[AF1] E. Acerbi - N. Fusco, Semicontinuity problems in the Calculus of Variations, Arch. Rational Mech. Anal. 86 (1984), 125-145. | MR | Zbl

[AF2] E. Acerbi - N. Fusco, A regularity theorem for minimizers of quasiconvex integrals, Arch. Rational Mech. Anal. 99 (1987), 261-281. | MR | Zbl

[AF3] E. Acerbi - N. Fusco, Partial regularity under anisotropic (p, q) growth conditions, J. Differential Equations 107 (1994), 46-67. | MR | Zbl

[AM1] E. Acerbi - G. Mingione, Regularity results for a class of functionals with nonstandard growth, Arch. Rational Mech. Anal. 156 (2001), 121-140. | MR | Zbl

[AM2] E. Acerbi - G. Mingione, Regularity results for electrorheological fluids: the stationary case, to appear. | MR

[A] Yu. A. Alkhutov, The Harnack inequality and the Hölder property of solutions of nonlinear elliptic equations with a nonstandard growth condition, Differential Equations 33 (1997), 1653-1663. | MR | Zbl

[BF] M. Bildhauer - M. Fuch, Partial regularity for variational integrals with (s, μ, q)-growth, Calc. Var., to appear. | Zbl

[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. | MR | Zbl

[CC] V. Chiadò Piat - A. Coscia, Hölder continuity of minimizers of functionals with variable growth exponent, Manuscripta Math. 93 (1997), 283-299. | MR | Zbl

[CM] A. Coscia - G. Mingione, Hölder continuity of the gradient of p(x)-harmonic mappings, C. R. Acad. Sci. Paris 328 (1999), 363-368. | MR | Zbl

[CFP] G. Cupini - N. Fusco - R. Petti, Hölder continuity of local minimizers, J. Math. Anal. Appl. 235 (1999), 578-597. | MR | Zbl

[Ek] I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc.1 (1979), 443-474. | MR | Zbl

[ELM] L. Esposito - F. Leonetti - G. Mingione, Higher integrability for minimizers of integralfunctionals with (p, q) growth, J. Differential Equations 157 (1999), 414-438. | MR | Zbl

[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 | MR | Zbl

[E] L. Evans, Quasiconvexity and partial regularity in the Calculus of Variations, Arch. Rational Mech. Anal. 95 (1986), 227-252. | MR | Zbl

[EG] L. Evans - R. Gariepy, Blow-up, compactness and partial regularity in the Calculus of Variations, Indiana Univ. Math. J. 36 (1987), 361-371. | MR | Zbl

[FZ] Fan Xiangling - Zhao Dun, A class of De Giorgi type and Hölder continuity, Nonlinear Anal. 36 (A) (1999), 295-318. | MR | Zbl

[FS] M. Fuchs - G. Seregin, A regularity theory for variational integrals with L log L-growth, Calc. Var. Partial Differential Equations 6 (1998), 171-187. | MR | Zbl

[FH] N. Fusco - J. Hutchinson, C1,α partial regularity of functions minimizing quasiconvex integrals, Manuscripta Math. 54 (1985), 121-143. | Zbl

[Gia] M. Giaquinta, "Multiple integrals in Calculus of Variations and nonlinear elliptic sistems", Annals of Math. Studies 105, Princeton Univ. Press, 1983. | MR | Zbl

[Giu] E. Giusti, "Metodi Diretti nel Calcolo delle Variazioni ", UMI, Bologna, 1994. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[M2] P. Marcellini, Regularity and existence of solutions of elliptic equations with p, q-growth conditions, J. Differential Equations 90 (1991), 1-30. | MR | Zbl

[M3] P. Marcellini, Regularity for elliptic equations with general growth conditions, J. Differential Equations 105 (1993), 296-333. | MR | Zbl

[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. | Numdam | MR | Zbl

[M5] P. Marcellini, Regularity for some scalar variational problems under general growth conditions, J. Optim. Theory Appl. 90 (1996), 161-181. | MR | Zbl

[RR] K.R. Rajagopal - M. Růžička, Mathematical modelling of electrorheological fluids, Cont. Mech. Therm. 13 (1) (2001), 59-78. | Zbl

[R1] M Růžička, Flow of shear dependent electrorheological, fluids, C. R. Acad. Sci. Paris 329 (1999), 393-398. | MR | Zbl

[R2] M Růžička, Electrorheological fluids: modeling and mathematical theory, Springer, Lecture Notes in Math. 1748 (2000). | MR | Zbl

[Z1] V.V. Zhikov, On Lavrentiev's phenomenon, Russian J. Math. Physics 3 (1995), 249-269. | MR | Zbl

[Z2] V.V. Zhikov, On some variational problems, Russian J. Math. Physics 5 (1997), 105-116. | MR | Zbl

[Z3] V.V. Zhikov, Meyers-type estimates for solving the non linear Stokes system, Differential Equations 33 (1) (1997), 107-114. | MR | Zbl