A regularity theorem for minimisers of quasiconvex integrals: The case 1 < p < 2

Royal Society of Edinburgh - Proceedings A

Volumn 126, Issue 6, 1996, Pages 1181-1199

  Carozza, Menita ^a   Passarelli Di Napoli, Antonia ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444439212     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500023350     Document Type: Article

References (17)

1. 1,p functions. Proceedings of the Symposium on Material Instabilities and Continuum Mechanics, ed. J. Ball, pp. 1-5 (Oxford Science Press, 1986).
2. E. Acerbi and N. Fusco. A regularity theorem for minimizers of quasiconvex integrals. Arch. Rational Mech. Anal. 99 (1987), 261-81.
3. E. Acerbi and N. Fusco. Regularity for minimizers of non-quadratic functional: the case 1 < p < 2. J. Math. Anal. Appl. 140 (1989), 115-35.
4. B. Dacorogna. Direct methods in the calculus of variations, Applied Mathematical Sciences 78 (Berlin: Springer, 1989).
5. G. Eisen. A selection lemma for sequences of measurable sets and lower semicontinuity of multiple integrals. Manuscripts math. 27 (1979), 73-9.
6. L. C. Evans. Quasiconvexity and partial regularity in the calculus of variations. Arch. Rational Mech. Anal. 95 (1986), 227-52.
7. L. C. Evans and R. F. Gariepy. Blow-up, compactness and partial regularity in the calculus of variations. Rend. Circ. Mat. Palermo (2) Suppl. 15 (1987), 101-8.
8. 1,x partial regularity of functions minimising quasiconvex integrals. Manuscripta Math. 54 (1985), 121-43.
9. N. Fusco and C. Sbordone. Higher integrability of the gradient of minimizers of functionals with nonstandard growth condition. Comm. Pure Appl. Math. 43 (1990), 673-83.
10. M. Giaquinta. Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies 105 (Princeton: Princeton University Press, 1983).
11. M. Giaquinta. Quasiconvexity, growth conditions and partial regularity, Lecture Notes in Mathematics 1357, eds. S. Hildebrandt and R. Leis, pp. 211-37 (Berlin: Springer, 1988).
12. M. Giaquinta and G. Modica. Partial regularity of minimizers of quasiconvex integrals. Ann. Inst. H. Poincaré, Anal. Non Linéaire 3 (1986), 185-208.
13. E. Giusti. Metodi diretti nel calcolo delle variazioni (Bologna: Unione Matematica Italiana, 1994).
14. M. C. Hong. Existence and partial regularity in the calculus of variations. Ann. Mat. Pura Appl. 149 (1987), 311-28.
15. P. Marcellini. Approximation of quasiconvex functions and lower semicontinuity of multiple integrals. Manuscripts Math. 51 (1986), 1-28.
16. C. B. Jr. Morrey. Multiple integrals in the calculus of variations (Berlin: Springer, 1966).
17. V. Sverak. Quasiconvex functions with subquadratic growth. Proc. Roy. Soc. London Ser. A 433 (1991), 723-5.