Regularity Results for a Class of Quasiconvex Functionals with Nonstandard Growth

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Volumn 30, Issue 2, 2001, Pages 311-339

  Acerbi, Emilio ^a   Mingione, Giuseppe ^a  

^a UNIVERSITY OF PARMA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845251994     PISSN: 0391173X     EISSN: 20362145     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. [AFI] E . ACERBI - N. Fusco, Semicontinuity problems in the Calculus of Variations, Arch. Rational Mech. Anal. 86 (1984), 125-145.
2. [AF2] E . ACERBI - N . Fusco, A regularity theorem for minimizers of quasiconvex integrals. Arch. Rational Mech. Anal. 99 (1987), 261-281.
3. [AF3] E . ACERBI - N. Fusco, Partial regularity under anisotropic (p, q) growth conditions, J. Differential Equations 107 (1994), 46-67.
4. [ A M 1 ] E . A C E R B I - G . MINGIONE, Regularity results for a class offunctionals with nonstandard growth. A r c h. Rational Mech. Anal. 1 5 6 (2001), 121-140.
5. [ A M 2 ] E . A C E R B I - G . MINGIONE, Regularity results for electrorheological fluids: the stationary case, to appear.
6. [A] Y u . A . ALKHUTOV, The Hamack inequality and the Holder property of solutions of nonlinear elliptic equations with a nonstandard growth condition. Differential Equations 33 (1997), 1653-1663.
7. [BF] M . BILDHAUER - M . FUCHS, Partial regularity for variational integrals with {s,ß,q)growth. Cale. Var., to appear.
8. [CFM] M. CAROZZA - N. Fusco - G. MINGIONE, Partial regularity ofminimizers ofquasiconvex integrals with subquadratic growth, Ann. Mat. Pura Appi. 175 (1998), 141-164.
9. [CC] V. GHIADO FIAT - A . Cosa A. Holder continuity ofminimizers offunctionals with variable growth exponent, Manuscripta Math. 93 (1997), 283-299.
10. [CM] A . COSCIA - G . MINGIONE, Holder continuity of the gradient of p(x)-harmonic mappings, C. R. Acad. Sci. Paris 3 2 8 (1999), 363-368.
11. [CFP] G. CUPINI - N . Fusco - R . PETTI, Holder continuity of local minimizers, J . Math. Anal. Appi. 2 3 5 (1999), 578-597.
12. [Ek] I . EKELAND, Nonconvex minimization problems. Bull. Amer. Math. Soc. 1 (1979), 443¬ 474.
13. [ELM] L . ESPOSITO - F . LEONETTI - G. MINGIONE, Higher integrability for minimizers of integralfunctional with (p, q) growth, J. Differential Equations 157 (1999), 414-438.
14. [EM] L . ESPOSITO - G. MINGIONE, Partial regularityfor minimizers ofconvex integrals with L log L-growth, NoDEA Nonlinear Differential Equations Appi. 7 (1) (2000), 107-125
15. [E] L . EVANS, Quasiconvexity and partial regularity in the Calculus of Variations, Arch. Rational Mech. Anal. 95 (1986), 227-252.
16. [EG] L . EVANS - R. GARIEPY, Blow-up, compactness andpartial regularity in the Calculus ofVariations, Indiana Univ. Math. J. 36 (1987), 361-371.
17. [FZ] FAN XIANGLING - ZHAO DUN, A class ofDe GiorgitypeandHoldercontinuity. Nonlinear Anal. 36 (A) (1999), 295-318.
18. [FS] M . FUCHS - G. SEREGIN, A regularity theory for variational integrals with LlogLgrowth. Cale. Var. Partial Differential Equations 6 (1998), 171-187.
19. [FH] N . Fusco - J . HUTCHINSON, C ^ partial regularity of functions minimizing quasiconvex integrals, Manuscripta Math. 54 (1985), 121-143.
20. [Gia] M. GiAQUiNTA, "Multiple integrals in Calculus of Variations and nonlinear elliptic sistems", Annals of Math. Studies 105, Princeton Univ. Press, 1983.
21. [Giu] E . GIUSTI, "Metodi Diretti nel Calcolo delle Variazioni", UMI, Bologna, 1994.
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.
23. [Ml] F . MARCELLINI, Regularity ofminimizers ofintegrals ofthe Calculus ofVariationswith non standard growth conditions. Arch. Rational Mech. Anal. 105 (1989), 267-284.
24. [M2] P. MARCELLINI, Regularity and existence of solutions of elliptic equations with p, q-growth conditions, J. Differential Equations 90 (1991), 1-30.
25. [M3] P. MARCELLINI, Regularity for elliptic equations with general growth conditions, J . Differential Equations 105 (1993), 296-333.
26. [M4] P. MARCELLINI, Everywhere regularity for a class of elliptic systems without growth conditions, Ann. Scuola Norm. Sup. Pisa CI. Sci. (4) 23 (1996), 1-25.
27. [M5] P. MARCELLINI, Regularity for some scalar variational problems under general growth conditions, J. Optim. Theory Appi. 90 (1996), 161-181.
28. [RR] K . R . RAJAGOPAL - M . RV1IC:KA, Mathematical modelling ofelectrorheological fluids, Cont. Mech. Therm. 13 (1) (2001), 59-78.
29. [ R l ] M. RÚZICKA, Flow ofshear dependent electrorheologicalfluids, C. R. Acad. Sci. Paris 3 2 9 (1999), 393-398.
30. [R2] M. RûziÎKA, Electrorheological fluids: modeling and mathematical theory. Springer, Lecture Notes in Math. 1748 (2000).
31. [ Z l ] V . V . ZHIKOV, On Lavrentiev's phenomenon, Russian J . Math. Physics 3 (1995), 249¬ 269.
32. [Z2] V. V. ZHIKOV, On some variationalproblems, Russian J . Math. Physics 5 (1997), 105¬ 116.
33. [Z3] V. V. ZHIKOV, Meyers-type estimatesfor solving the non linear Stokes system. Differential Equations 33 (1) (1997), 107-114.