Regularity of minimizers for nonconvex vectorial integrals with p-q growth via relaxation methods

Abstract and Applied Analysis

Volumn 2004, Issue 1, 2004, Pages 27-44

  Benedetti, Irene ^a   Mascolo, Elvira ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942535974     PISSN: 10853375     EISSN: None     Source Type: Journal    
DOI: 10.1155/S1085337504310079     Document Type: Article

References (14)

1. G. Buttazzo and V. J. Mizel, Interpretation of the Lavrentiev phenomenon by relaxation, J. Funct. Anal. 110 (1992), no. 2, 434-460.
2. G. Cupini, M. Guidorzi, and E. Mascolo, Regularity of minimizers of vectorial integrals with p-q growth, Nonlinear Anal. 54 (2003), no. 4, 591-616.
3. G. Cupini and A. P. Migliorini, Holder continuity for local minimizers of a nonconvex variational problem, J. Convex Anal. 10 (2003), no. 2, 389-408.
4. B. Dacorogna, Direct Methods in the Calculus of Variations, Applied Mathematical Sciences, vol. 78, Springer-Verlag, Berlin, 1989.
5. E. De Giorgi, Sulla convergenza di alcune successioni d'integrali del tipo dell'area, Rend. Mat. (6) 8 (1975), 277-294 (Italian).
6. L. Esposito, F. Leonetti, and G. Mingione, Regularity results for minimizers of irregular integrals with (p,q) growth, Forum Math. 14 (2002), no. 2, 245-272.
7. I. Fonseca, N. Fusco, and P. Marcellini, An existence result for a nonconvex variational problem via regularity, ESAIM Control Optim. Calc. Var. 7 (2002), 69-95.
8. I. Fonseca and J. Malý, Relaxation of multiple integrals below the growth exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), no. 3, 309-338.
9. N. Fusco, On the convergence of integral functionals depending on vector-valued functions, Ricerche Mat. 32 (1983), no. 2, 321-339.
10. E. Giusti, Metodi Diretti nel Calcolo delle Variazioni [Direct Methods in the Calculus of Variations], Unione Matematica Italiana, Bologna, 1994 (Italian).
11. P. Marcellini, Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals, Manuscripta Math. 51 (1985), no. 1-3, 1-28.
12. _, Regularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions, Arch. Ration. Mech. Anal. 105 (1989), no. 3, 267-284.
13. E. Mascolo and A. P. Migliorini, Everywhere regularity for vectorial functionals with general growth, ESAIM Control Optim. Calc. Var. 9 (2003), 399-418.
14. E. Mascolo and R. Schianchi, Existence theorems in the calculus of variations, J. Differential Equations 67 (1987), no. 2, 185-198.