Free Access
Issue
ESAIM: COCV
Volume 9, March 2003
Page(s) 125 - 133
DOI https://doi.org/10.1051/cocv:2003003
Published online 15 September 2003
  1. M. Bardi and I. Capuzzo Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser, Boston (1997). [Google Scholar]
  2. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Springer Verlag, Berlin (1994). [Google Scholar]
  3. P. Bauman and D. Phillips, A non-convex variational problem related to change of phase. Appl. Math. Optim. 21 (1990) 113-138. [CrossRef] [MathSciNet] [Google Scholar]
  4. P. Cardaliaguet, B. Dacorogna, W. Gangbo and N. Georgy, Geometric restrictions for the existence of viscosity solutions. Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999) 189-220. [CrossRef] [MathSciNet] [Google Scholar]
  5. P. Celada, Some scalar and vectorial problems in the Calculus of Variations, Ph.D. Thesis. SISSA, Trieste (1997). [Google Scholar]
  6. P. Celada and A. Cellina, Existence and non existence of solutions to a variational problem on a square. Houston J. Math. 24 (1998) 345-375. [MathSciNet] [Google Scholar]
  7. P. Celada, S. Perrotta and G. Treu, Existence of solutions for a class of non convex minimum problems. Math. Z. 228 (1998) 177-199. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Cellina, Minimizing a functional depending on ∇u and on u. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 339-352. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Cellina and S. Perrotta, On minima of radially symmetric functionals of the gradient. Nonlinear Anal. 23 (1994) 239-249. [CrossRef] [MathSciNet] [Google Scholar]
  10. G. Crasta, On the minimum problem for a class of non-coercive non-convex variational problems. SIAM J. Control Optim. 38 (1999) 237-253. [CrossRef] [MathSciNet] [Google Scholar]
  11. G. Crasta, Existence, uniqueness and qualitative properties of minima to radially symmetric non-coercive non-convex variational problems. Math. Z. 235 (2000) 569-589. [CrossRef] [MathSciNet] [Google Scholar]
  12. G. Crasta and A. Malusa, Euler-Lagrange inclusions and existence of minimizers for a class of non-coercive variational problems. J. Convex Anal. 7 (2000) 167-181. [MathSciNet] [Google Scholar]
  13. G. Crasta and A. Malusa, Non-convex minimization problems for functionals defined on vector valued functions. J. Math. Anal. Appl. 254 (2001) 538-557. [CrossRef] [MathSciNet] [Google Scholar]
  14. B. Dacorogna and P. Marcellini, Existence of minimizers for non-quasiconvex integrals. Arch. Rational Mech. Anal. 131 (1995) 359-399. [CrossRef] [MathSciNet] [Google Scholar]
  15. B. Kawohl, J. Stara and G. Wittum, Analysis and numerical studies of a problem of shape design. Arch. Rational Mech. Anal. 114 (1991) 349-363. [CrossRef] [MathSciNet] [Google Scholar]
  16. R. Kohn and G. Strang, Optimal design and relaxation of variational problems, I, II and III. Comm. Pure Appl. Math. 39 (1976) 113-137, 139-182, 353-377. [CrossRef] [MathSciNet] [Google Scholar]
  17. P.L. Lions, Generalized solutions of Hamilton-Jacobi equations. Pitman, London, Pitman Res. Notes Math. Ser. 69 (1982). [Google Scholar]
  18. E. Mascolo and R. Schianchi, Existence theorems for nonconvex problems J. Math. Pures Appl. 62 (1983) 349-359. [Google Scholar]
  19. R.T. Rockafellar, Convex Analysis. Princeton Univ. Press, Princeton (1970). [Google Scholar]
  20. G. Treu, An existence result for a class of non convex problems of the Calculus of Variations. J. Convex Anal. 5 (1998) 31-44. [MathSciNet] [Google Scholar]
  21. M. Vornicescu, A variational problem on subsets of Formula . Proc. Roy. Soc. Edinburg Sect. A 127 (1997) 1089-1101. [Google Scholar]

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