Regularity results for minimizers of irregular integrals with (p, q) growth

Forum Mathematicum

Volumn 14, Issue 2, 2002, Pages 245-272

  Esposito, Luca ^a   Leonetti, Francesco ^b   Mingione, Giuseppe ^c  

^a UNIVERSITY OF SALERNO   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

^c UNIVERSITY OF PARMA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036102396     PISSN: 09337741     EISSN: None     Source Type: Journal    
DOI: 10.1515/form.2002.011     Document Type: Article

References (26)

1. [AF] Acerbi, E. and Fusco, N.: Regularity of minimizers of non-quadratic functionals: the case 1 < p < 2. J. Math. Anal. Appl. 140 (1989), 115-135
2. [Ch] Choe, H. J.: Interior behavior of minimizers for certain functionals with non standard growth. Nonlinear Anal. 19 (1992), 933-945
3. [CF] Cianchi, A. and Fusco, N.: Gradient regularity for minimizers under general growth conditions. J. Reine Angew. Math. 509 (1999), 15-36
4. [EM] Esposito, L. and Mingione, G.: Some remarks on the regularity of weak solutions of degenerate elliptic systems. Rev. Mat. Complutense Madrid 11 (1998), 103-119
5. [ELM] Esposito, L., Leonetti, F., Mingione, G.: Higher integrability-for minimizers of integral functionals with (p,q) growth. J. Differential Equations 157 (1999), 414-438
6. [FF] Fonseca, I. and Fusco, N.: Regularity result for anisotropic image segmentation models. Ann. Sc. Norm. Sup. Pisa 24 (1997), 463-499
7. [FL] Fuchs, M. and Li, G.: Global gradient bounds for relaxed variational problems. Manuscripta Math. 92 (3) (1997), 287-302
8. [FMT] Fusco, N., Mingione, G. and Trombetti, C.: Regularity of minimizers for a class of anisotropic free discontinuity problems preprint. Journal of Convex Analysis 8 (2001)
9. [Gia1] Giaquinta, M.: Multiple integrals in the Calculus of Variations and nonlinear elliptic systems. Annals of Mathematics Studies 105. Princeton University Press, Princeton, 1983
10. [Gia2] Giaquinta, M.: Growth conditions and regularity, a counterexample. Manuscripta Math. 59 (1987), 245-248
11. [GM] Giaquinta, M. and Modica, G.: Remarks on the regularity of the minimizers of certain degenerate functionals. Manuscripta Math. 57 (1986), 55-99
12. [GT] Gilbarg, D. and Trudinger, N. S.: Elliptic partial differential equations of second order. Grundlehren der Math. Wiss. 224. Springer, 1977
13. [G] Giusti, E.: Metodi diretti nel calcolo delle variazioni. UMI, Bologna, 1994
14. [H] Hong, M. C.: Some remarks on the minimizers of variational integrals with non standard growth conditions. Boll. Un. Mat. Ital. 6-A (1992), 91-101
15. [L] Lieberman, G.: The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations. Comm. Partial Differential Equations 16 (1991), 311-361
16. [Ma] Manfredi, J.: Regularity for minima of functionals with p-growth. J. Differential Equations 76 (1988), 203-212
17. [M1] Marcellini, P.: Regularity and existence of solutions of elliptic equations with p,q-growth conditions. J. Differential Equations 90 (1991), 1-30
18. [M2] Marcellini, P.: Regularity for elliptic equations with general growth conditions. J. Differential Equations 105 (1993), 296-333
19. [M3] Marcellini, P.: Everywhere regularity for a class of elliptic systems without growth conditions. Ann. Scuola Norm. Sup. Pisa 23 (1996), 1-25
20. [M4] Marcellini, P.: Regularity for some scalar variational problems under general growth conditions. J. Optim. Theory Appl. 90 (1996), 161-181
21. [M5] Marcellini, P.: Regularity of minimizers of integrals of the Calculus of Variations with non standard growth conditions. Arch. Rat. Mech. Anal. 105 (1989), 267-284
22. [M6] Marcellini, P.: Un example de solution discontinue d'un probleme variationnel dans le cas scalaire. Preprint Istituto Matematico U. Dini, Universita' di Firenze, 1987/88, n. 11
23. [MP] Mascolo, E. and Papi, G.: Local boundedness of minimizers of integrals of the Calculus of Variations. Ann. Mat. Pura Appl. 167 (1994), 323-339
24. [S] Siepe, F.: Regularity of minimizers of a class of anisotropic integral functionals. Preprint Univ. Firenze No. 5, 1998
25. [T] Talenti, G.: Buondedness of minimizers. Hokkaido Math. J. 19 (1990), 259-279
26. [U] Uhlenbeck, K.: Regularity for a class of nonlinear elliptic systems. Acta Math. 138 (1977), 219-240