Gradient estimates for the p(x)-Laplacean system

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 584, 2005, Pages 117-148

  Acerbi, Emilio ^a   Mingione, Giuseppe ^a  

^a UNIVERSITY OF PARMA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27844601209     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/crll.2005.2005.584.117     Document Type: Article

References (36)

1. E. Acerbi and N. Fusco, Regularity for minimizers of nonquadratic functionals: the case 1 < p < 2, J. Math. Anal. Appl. 140 (1989), 115-135.
2. E. Acerbi and G. Mingione, Regularity results for a class of functionals with non-standard growth, Arch. Rat. Mech. Anal. 156 (2001), 121-140.
3. E. Acerbi and G. Mingione, Regularity results for stationary electro-rheological fluids, Arch. Rat. Mech. Anal. 164 (2002), 213-259.
4. E. Acerbi, G. Mingione and G. A. Seregin, Regularity results for parabolic systems related to a class of Non Newtonian fluids, Ann. Inst. H. Poincaré Anal. Non Lin. 21 (2004), 25-60.
5. K. Astala, T. Iwaniec, P. Koskela and G. Martin, Mappings of BMO-bounded distortion, Math. Ann. 317 (2000), 703-726.
6. n, Ann. Acad. Sci. Fenn. (A I Math.) 8 (1983), 257-324.
7. L. Caffarelli, Interior a priori estimates for solutions of fully nonlinear equations, Ann. Math. 130 (1989), 189-213.
8. 1,p estimates for elliptic equations in divergence form, Comm. Pure Appl. Math. 51 (1998), 1-21.
9. A. Coscia and G. Mingione, Hölder continuity of the gradient of p(x)-harmonic mappings, C. R. Acad. Sci. Paris (I Math.) 328 (1999), 363-368.
10. p spaces, Ann. Acad. Sci. Fenn. (A I Math.) 28 (2003), 223-238.
11. G. Cupini, N. Fusco and R. Petti, Hölder continuity of local minimizers, J. Math. Anal. Appl. 235 (1999), 578-597.
12. p(.) and problems related to fluid dynamics, J. reine angew. Math. 563 (2003), 197-220.
13. p(.), I and II, J. Math. Anal. Appl. 298 (2004) no 2, 559-571 and 572-588.
14. D. Edmunds and J. Rakosnik, Sobolev embeddings with variable exponent, Stud. Math. 143 (2000), 267-293.
15. L. Esposito, F. Leonetti and G. Mingione, Higher integrability for minimizers of integral functionals with (p,q) growth, J. Diff. Equ. 157 (1999), 414-438.
16. E. Giusti, Direct methods in the calculus of variations, World Scientific Publishing Co., Inc., River Edge, NJ, 2003.
17. P. Harjulehto, P. Hästö and O. Martio, Fuglede's theorem in variable exponent Sobolev space, Collect. Math. 55 (2004) no 3, 315-324.
18. P. Hästö , Counter-examples of regularity in variable exponent Sobolev spaces, Contemp. Math., to appear.
19. p-estimates for degenerated elliptic operators, Stud. Math. 75 (1983), 293-312.
20. T. Iwaniec, p-harmonic tensors and quasiregular mappings, Ann. Math. (2) 136 (1992), 589-624.
21. T. Iwaniec, The Gehring lemma, Quasiconformal mappings and analysis (Ann Arbor, MI, 1995), Springer, New York (1998), 181-204.
22. T. Iwaniec and A. Verde, On the operator ℒ(f) = f log|f|, J. Funct. Anal. 169 (1999), 391-420.
23. J. Kinnunen and S. Zhou, A local estimate for nonlinear equations with discontinuous coefficients, Comm. Part. Diff. Equ. 24 (1999), 2043-2068.
24. S. Levine, J. Stanich and Y. Chen, Image restoration via non standard diffusion, to appear.
25. J. J. Manfredi, Regularity for minima of functionals with p-growth, J. Diff. Equ. 76 (1988), 203-212.
26. P. Marcellini, Regularity and existence of solutions of elliptic equations with p,q-growth conditions, J. Diff. Equ. 90 (1991), 1-30.
27. p(x) on which the Hardy-Littlewood maximal operator is not bounded, Expo. Math. 19 (2001), 369-371.
28. K. R. Rajagopal and M. Růžička, Mathematical modeling of electrorheological materials, Contin. Mech. Thermodyn. 13 (2001), 59-78.
29. M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Monogr. Textb. Pure Appl. Math. 146, Marcel Dekker, Inc., New York 1991.
30. M. Růžička, Electrorheological fluids: modeling and mathematical theory, Springer Lect. Notes Math. 1748 (2000).
31. M. Růžička, Flow of shear dependent electrorheological fluids, C. R. Acad. Sci. Paris (I Math.) 329 (1999), 393-398.
32. E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton University Press, Princeton, NJ, 1993.
33. K. Uhlenbeck, Regularity for a class of non-linear elliptic systems, Acta Math. 138 (1977), 219-240.
34. N. Ural'tseva, Quasilinear degenerate systems (russian), Leningrad Odtel. Mat. Inst. Steklov (LOMI) 7 (1968), 184-222.
35. V. V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory (russian), Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), 675-710, 877.
36. V. V. Zhikov, On Lavrentiev's phenomenon, Russian J. Math. Phys. 3 (1995), 249-269.