Hölder continuity of local minimizers of vectorial integral functional

Nonlinear Differential Equations and Applications

Volumn 10, Issue 3, 2003, Pages 269-285

  Cupini, Giovanni ^a   Petti, Raffaella ^a  

^a Dip di Matematica   (Italy)

Author keywords

H lder continuity; Local minimizer; Regularity

Indexed keywords

EID: 0141642230     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00030-003-1025-x     Document Type: Article

References (21)

1. E. ACERBI, N. FUSCO. Regularity of minimizers of non-quadratic functionals: the case 1 < p < 2, J. Math. Anal. Appl. 140 (1989), 115-135.
2. S. CAMPANATO, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa. 17 (1963), 157-188.
3. G. CUPINI, N. FUSCO, R. PETTI, Hölder continuity of local minimizers, J. Math. Anal. Appl. 235 (1999), 578-597.
4. I. EKELAND, Nonconvex minimization problems, Bull. Amer. Math. Soc. 1 (1979), 443-474.
5. 1,α regularity of minimizers, Ricerche Mat. 45 (1996), 311-327.
6. L. ESPOSITO, F. LEONETTI, G. MINGIONE, Regularity results for minimizers of irregular integrals with (p, q) growth, Forum Mathematicum 14 (2002), 245-272.
7. I. FONSECA, N. FUSCO, Regularity results for anisotropic image segmentation models, Ann. Scuola Norm. Sup. Pisa 24 (1997), 463-499.
8. I. FONSECA, N. FUSCO, P. MARCELLINI, An existence result for a non-convex variational problem via regularity, Control, Optimization and Calculus of Variations. 7 (2002), 69-95.
9. N. FUSCO, J. HUTCHINSON, Partial regularity for minimisers of certain functional having nonquadratic growth, Ann. Mat. Pura Appl. 155 (1989), 1-24.
10. N. FUSCO, G. MINGIONE, C. TROMBETTI, Regularity of minimizers for a class of anisotropic free discontinuity problems, J. Convex Anal. 8 (2001).
11. M. GIAQUINTA, "Multiple integrals in calculus of variations and nonlinear elliptic systems", Ann. of Math. Stud. 105, Princeton Univ. Press 1983.
12. M. GIAQUINTA, E. GIUSTI, Nonlinear elliptic systems with quadratic growth, Manuscripta Math. 24 (1978), 323-349.
13. M. GIAQUINTA, E. GIUSTI, On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31-46.
14. M. GIAQUINTA, E. GIUSTI, Differentiability of minima of non-differentiable functionals, Invent. Math. 72 (1983), 285-298.
15. M. GIAQUINTA, E. GIUSTI, Quasi-minima, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), 79-107.
16. M. GIAQUINTA, G. MODICA, Remarks on the regularity of the minimizers of certain degenerate functionals, Manuscripta Math. 57 (1986), 55-99.
17. M. GIAQUINTA, J. SOUČEK, Harmonic maps into a hemisphere, Ann. Scuola Norm. Sup. Pisa 12 (1985), 81-90.
18. 1,p e singolarità delle soluzioni deboli di sistemi elittici non lineari, Boll. Un. Mat. Ital. 2 (1969), 71-76.
19. E. GIUSTI, "Metodi diretti nel calcolo delle variazioni", U.M.I., Bologna 1994.
20. J.J. MANFREDI, Regularity for minima of functionals with p-growth, J. Differential Equations 76 (1988), 203-212.
21. R. SCHOEN, K. UHLENBECK, Regularity of minimizing harmonic maps into the sphere, Invent. Math. 78 (1984), 89-100.