Some remarks about relaxation problems in the Calculus of Variations

Royal Society of Edinburgh - Proceedings A

Volumn 126, Issue 3, 1996, Pages 665-675

  Flores Bazán, Fabián ^a  

^a UNIVERSITY OF CONCEPCIÓN   (Chile)

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EID: 21344451725     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500022964     Document Type: Article

References (26)

1. E. A. Acerbi and N. Fusco. Semicontinuity problems in Calculus of Variations. Arch. Rational Mech. Anal. 86 (1984), 125-45.
2. S. Agmon, A. Douglis and L. Nirenberg. Estimates near the boundary for the solutions of elliptic differential equations satisfying general boundary values I and II. Commun. Pure Appl. Math. 12 (1959), 623-727;
3. S. Agmon, A. Douglis and L. Nirenberg. Commun. Pure Appl. Math. 17 (1964), 35-92.
4. M. Amar and V. De Cicco. Relaxation of quasiconvex integrals of arbitrary order. Proc. Roy. Soc. Edinburgh Sect. A 124, (1994), 927-46.
5. G. Aubert and R. Tahraoui. Théorèmes d'existence en Optimisation non Convexe. Appl. Anal. 18 (1984), 75-100.
6. G. Aubert and R. Tahraoui. Sur une classe de problèmes différentiels non linéaires par une méthode variationnelle. Bol. Un. Mat. Ital. 7(3-B) (1989), 739-57.
7. J. M. Ball, J. C. Currie and P. J. Olivier. Null Lagrangian, weak continuity, and variational problems of arbitrary order. J. Funct. Anal. 41 (1981), 135-74.
8. H. Brézis. Analyse Fonctionnelle (Paris: Masson, 1987).
9. G. Buttazzo and A. Leaci. Relaxation results for a class of variational integrals. J. Funct. Anal. 61 (1985), 360-77.
10. G. Buttazzo. Some relaxation problems in optimal control theory. J. Math. Anal. Appl. 125 (1987), 272-87.
11. G. Buttazzo. Semicontinuity, relaxation and integral representation in the Calculus of Variations, Pitman Research Notes in Mathematics 207 (Harlow: Longman, 1989).
12. A. Cellina and F. Flores. Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions. Ann. Inst. H. Poincaré, Anal. Non Linéaire 9 (1992), 465-78.
13. B. Dacorogna. Weak continuity and weak lower Semicontinuity of nonlinear functionals, Lecture Notes in Mathematics 922 (Berlin: Springer, 1982).
14. B. Dacorogna. Quasiconvexity and relaxation of nonconvex problems in the Calculus of Variations. J. Funct. Anal. 46 (1982), 102-18.
15. G. Dal Maso. An Introduction to Γ-convergence (Boston: Birkhäuser, 1993).
16. I. Ekeland. Sur le contrôle optimal de systèmes par des equations elliptiques. J. Funct. Anal. 9 (1972), 1-62.
17. G. Eisen. A selection lemma for sequences of measurable sets, and lower Semicontinuity of multiple integrals. Manuscripta Math. 27 (1979), 73-9.
18. I. Ekeland and R. Temam. Convex Analysis and Variational Problems (Amsterdam: North-Holland, 1976).
19. F. Flores. On radial solutions for non-convex variational problems (To appear in Houston J. Math.).
20. p). Proc. Roy. Soc. Edinburgh Sect. A 121 (1992), 321-48.
21. D. Gilbarg and N. Trudinger. Elliptic Partial Differential Equations of Second Order (Berlin: Springer, 1983).
22. P. Marcellini and C. Sbordone. Semicontinuity problems in the calculus of variations. Nonlinear Anal. 4 (1980), 241-57.
23. D. Percivale. A remark on relaxation of integral functionals. Nonlinear Anal. 16 (1991), 791-3.
24. P. J. Rabier. New existence results for some nonconvex optimization problems. Com. Partial Differential Equations 14 (1989), 699-740.
25. J. P. Raymond. Problèmes de Calcul des Variations et de Contrôle Optimal: Existence et Regularité des Solutions (Thèse d'habilitation, Université Paul Sabatier, Toulouse, 1990).
26. M. Valadier. Régularisation s.c.i., relaxation et théorèmes bang-band. C.R. Acad. Sci. Paris Sér. I Math. 293(2) (1981), 115-16.