Maximum principle for vector valued minimizers

Journal of Convex Analysis

Volumn 12, Issue 2, 2005, Pages 267-278

  Leonetti, Francesco ^a   Siepe, Francesco ^b  

^a UNIVERSITY OF L'AQUILA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Calculus of variations; Maximum principle; Minimizers; Rank one convexity; Relaxation

Indexed keywords

EID: 32044442481     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. 1,p-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984) 225-253.
2. G. Buttazzo: Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Res. Notes in Math. 207, Longman, Harlow (1989).
3. B. Dacorogna: Direct Methods in the Calculus of Variations, Applied Mathematical Sciences 78, Springer, Berlin (1989).
4. L. Esposito, G. Mingione: Partial regularity for minimizers of degenerate polyconvex energies, J. Convex Analysis 8 (2001) 1-38.
5. N. Fusco, J. Hutchinson: Partial regularity and everywhere continuity for a model problem from non-linear elasticity, J. Aust. Math. Soc., Ser. A 57 (1994) 158-169.
6. N. Fusco, J. Hutchinson: A direct proof for lower semicontinuity of polyconvex functionals, Manuscripta Math. 87(1) (1995) 35-50.
7. F. Leonetti: Maximum principle for vector-valued minimizers of some integral functionals, Boll. Un. Mat. Ital. 7 (1991) 51-56.
8. J. Maly: Weak lower semicontinuity of polyconvex integrals, Proc. Roy. Soc. Edinburgh, Sect. A 123(4) (1993) 681-691.
9. P. Marcellini: On the definition and the lower semicontinuity of certain quasiconvex integrals, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 3 (1986) 391-409.
10. V. Sverak: Personal communication (1993).