On improved regularity of weak solutions of some degenerate, anisotropie elliptic systems

Annali di Matematica Pura ed Applicata

Volumn 170, Issue 1, 1996, Pages 241-255

  Bhattacharya, Tilak ^a   Leonetti, Francesco ^b  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007031429     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/BF01758990     Document Type: Article

References (20)

1. E. ACERBI - N. Fusco, Regularity for minimizers of non-quadratic functionals: the case 1 p < 2, J. Math. Anal. Appl, 140 (1989), pp. 115-135.
2. R. A. ADAMS, Sobolev Spaces, New York (1975).
3. T. BHATTACHARYA - F. LEONETTI, W2> 2 regularity for iveak solutions of elliptic systems with nonstandard growth, J. Math. Anal. Appl., 176 (1993), pp. 224-234.
4. T. BHATTACHARYA - F. LEONETTI, Some remarks on the regularity of minimizers of integrals with anisotropic growth, Comment. Math. Univ. Carolinae, 34 (1993), pp. 597-611.
5. S. CAMPANATO, Sistemi ellittici informa divergenza, Regolarità aU'interno, Quaderni Scuola Normale Superiors, Pisa (1980).
6. S. CAMPANATO, Holder continuity of the solutions of some nonlinear elliptic systems, Adv. Math., 48 (1983), pp. 16-43.
7. S. CAMPANATO - P. CANNARSA, Differentiability and partial holder continuity of the solutions of nonlinear elliptic systems of order 2m with quadratic growth, Ann. Scuola Norm. Sup. Pisa, 8 (1981), pp. 285-309.
8. F. DE THELIN, Régularité de la solution d'une equation fortement (ou faiblement) non linéaire dans R", Ann. Fac. Se. Toulouse, 2 (1980), pp. 249-281.
9. F. DE THELIN, Local regularity properties for the solutions of a nonlinear partial differential equation, Nonlinear Analysis T.M.A., 6 (1982), pp. 839-844.
10. N. Fusco - C. SBORDONE, Local boundedness of minimizers in a limit case, Manuscripts Math., 69 (1990), pp. 19-25.
11. N. Fusco - C. SBORDONE, Some remarks on the regularity of minima of anisotropic integrals, Comm. Partial Differential Equations, 18 (1993), pp. 153-167.
12. M. GIAQUINTA, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. Math. Studies, 105, Princeton University Press, Princeton (1983).
13. M. GIAQUINTA, Growth conditions and regularity, a counterexample, Manuscripta Math., 59 (1987), pp. 245-248.
14. F. LEONETTI, Higher integrability for minimizers of integral functionals with nonstandard groivth, J. Differential Equations, 112 (1994), pp. 308-324.
15. P. MARCELLINI, Un exemple de solution discontinue d'un problème variationnel dans le cas scalaire, preprint Istituto Matematico U. Dini, Université di Firenze (1987/88), n. 11.
16. P. MARCELLINI, Regularity of minimizers of integrals of the calculus of variations with nonstandard groivth conditions, Arch. Rational Mech. Anal., 105 (1989), pp. 267- 284.
17. J. NAUMANN, Interior integral estimates on iveak solutions of certain degenerate elliptic systems, Ann. Mat. Pura Appl., 156 (1990), pp. 113-125.
18. J. P. RAYMOND, Théorèmes de régularité locale pour des systèmes elliptiques dégénérés et des problèmes non differentiates, Ann. Fac. Se. Toulouse, 9 ((1988), pp. 381- 412.
19. P. TOLKSDORF, Everywhere-regularity for some quasilinear systems with a lack of ellipticity, Ann. Mat. Pura Appl., 134 (1983), pp. 241-266.
20. P. TOLKSDORF, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations, 51 (1984), pp. 126-150.