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Volumn 130, Issue 4, 2000, Pages 721-741

Minimizing non-convex multiple integrals: A density result

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EID: 23044520958     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s030821050000038x     Document Type: Article
Times cited : (15)

References (29)
  • 1
    • 0042044425 scopus 로고    scopus 로고
    • Existence and regularity of minimizers of non convex functional depending on u and ∇u
    • P. Celada. Existence and regularity of minimizers of non convex functional depending on u and ∇u. J. Math. Analysis Appl. 230 (1999), 30-56.
    • (1999) J. Math. Analysis Appl. , vol.230 , pp. 30-56
    • Celada, P.1
  • 2
    • 0032443214 scopus 로고    scopus 로고
    • Existence and non existence of solutions to a variational problem on a square
    • P. Celada and A. Cellina. Existence and non existence of solutions to a variational problem on a square. Houston J. Math. 24 (1996), 345-375.
    • (1996) Houston J. Math. , vol.24 , pp. 345-375
    • Celada, P.1    Cellina, A.2
  • 3
    • 0032222402 scopus 로고    scopus 로고
    • Existence of solutions for a class of non convex minimum problems
    • P. Celada, S. Perrotta and G. Treu. Existence of solutions for a class of non convex minimum problems. Math. Z. 228 (1998), 177-199.
    • (1998) Math. Z. , vol.228 , pp. 177-199
    • Celada, P.1    Perrotta, S.2    Treu, G.3
  • 4
    • 38249004838 scopus 로고
    • On minima of a functional of the gradient: Necessary conditions
    • A. Cellina. On minima of a functional of the gradient: necessary conditions. Nonlinear Analysis 20 (1993), 337-341.
    • (1993) Nonlinear Analysis , vol.20 , pp. 337-341
    • Cellina, A.1
  • 5
    • 38249005312 scopus 로고
    • On minima of a functional of the gradient: Sufficient conditions
    • A. Cellina. On minima of a functional of the gradient: sufficient conditions. Nonlinear Analysis 20 (1993), 343-347.
    • (1993) Nonlinear Analysis , vol.20 , pp. 343-347
    • Cellina, A.1
  • 7
    • 84966246898 scopus 로고
    • The existence question in the calculus of variations: A density result
    • A. Cellina. and C. Mariconda. The existence question in the calculus of variations: a density result. Proc. Am. Math. Soc. 120 (1994), 1145-1150.
    • (1994) Proc. Am. Math. Soc. , vol.120 , pp. 1145-1150
    • Cellina, A.1    Mariconda, C.2
  • 8
    • 0000780871 scopus 로고
    • On minima of radially symmetric functionals of the gradient
    • A. Cellina. and S. Perrotta. On minima of radially symmetric functionals of the gradient. Nonlinear Analysis 23 (1994), 239-249.
    • (1994) Nonlinear Analysis , vol.23 , pp. 239-249
    • Cellina, A.1    Perrotta, S.2
  • 9
    • 84974403712 scopus 로고
    • Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations
    • M. Chipot. and L. C. Evans. Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations. Proc. R. Soc. Edinb. A 102 (1986), 291-303.
    • (1986) Proc. R. Soc. Edinb. A , vol.102 , pp. 291-303
    • Chipot, M.1    Evans, L.C.2
  • 10
    • 0011216933 scopus 로고    scopus 로고
    • On the Dirichlet problem for Hamilton-Jacobi equations. A Baire category approach
    • F. S. De Blasi and G. Pianigiani. On the Dirichlet problem for Hamilton-Jacobi equations. A Baire category approach. NoDEA Nonlinear Diff. Eqns Appl. 6 (1999), 13-34.
    • (1999) NoDEA Nonlinear Diff. Eqns Appl. , vol.6 , pp. 13-34
    • De Blasi, F.S.1    Pianigiani, G.2
  • 11
    • 84973960437 scopus 로고
    • A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems
    • G. Friesecke. A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems. Proc. R. Soc. Edinb. A 124 (1994), 437-471.
    • (1994) Proc. R. Soc. Edinb. A , vol.124 , pp. 437-471
    • Friesecke, G.1
  • 12
    • 0000602302 scopus 로고    scopus 로고
    • Existence of minimizers for some non convex one dimensional integrals
    • N. Fusco, P. Marcellini and A. Ornelas. Existence of minimizers for some non convex one dimensional integrals. Portugal Math. 55 (1998), 167-185.
    • (1998) Portugal Math. , vol.55 , pp. 167-185
    • Fusco, N.1    Marcellini, P.2    Ornelas, A.3
  • 13
    • 0001812542 scopus 로고
    • On the regularity of the minima of variational integrals
    • M. Giaquinta and E. Giusti. On the regularity of the minima of variational integrals. Acta Math. 148 (1982), 31-46.
    • (1982) Acta Math. , vol.148 , pp. 31-46
    • Giaquinta, M.1    Giusti, E.2
  • 14
    • 0022766604 scopus 로고
    • Numerical study of a relaxed variational problem from optimal design
    • J. Goodman, R. V. Kohn and L. Reyna. Numerical study of a relaxed variational problem from optimal design. Comput. Methods Appl. Mech. Engng 57 (1986), 107-127.
    • (1986) Comput. Methods Appl. Mech. Engng , vol.57 , pp. 107-127
    • Goodman, J.1    Kohn, R.V.2    Reyna, L.3
  • 16
    • 34250523511 scopus 로고
    • On some non linear elliptic differential-functional equations
    • P. Hartman and G. Stampacchia. On some non linear elliptic differential-functional equations. Acta Math. 115 (1966), 271-310.
    • (1966) Acta Math. , vol.115 , pp. 271-310
    • Hartman, P.1    Stampacchia, G.2
  • 17
    • 0000439529 scopus 로고
    • Analysis and numerical studies of a problem of shape design
    • B. Kawhol, J. Stara and G. Wittum. Analysis and numerical studies of a problem of shape design. Arch. Ration. Mech. Analysis 114 (1991), 349-363.
    • (1991) Arch. Ration. Mech. Analysis , vol.114 , pp. 349-363
    • Kawhol, B.1    Stara, J.2    Wittum, G.3
  • 18
    • 84987788617 scopus 로고
    • A relation between existence of minima for non convex integrals and uniqueness for non strictly convex integrals of the calculus of variations
    • Mathematical theories of optimization (ed. J. P. Cecconi and T. Zolezzi), Springer
    • P. Marcellini. A relation between existence of minima for non convex integrals and uniqueness for non strictly convex integrals of the calculus of variations. In Mathematical theories of optimization (ed. J. P. Cecconi and T. Zolezzi), vol. 979, pp. 216-231. Lecture Notes in Mathematics (Springer, 1983).
    • (1983) Lecture Notes in Mathematics , vol.979 , pp. 216-231
    • Marcellini, P.1
  • 19
    • 38249034964 scopus 로고
    • Existence theorems in the calculus of variations
    • E. Mascolo and R. Schianchi. Existence theorems in the calculus of variations. J. Diff. Eqns 67 (1987), 185-198.
    • (1987) J. Diff. Eqns , vol.67 , pp. 185-198
    • Mascolo, E.1    Schianchi, R.2
  • 20
    • 21844514093 scopus 로고
    • Genericity and existence of a minimum for scalar integrals functionals
    • M. D. P. Monteiro Marques and A. Ornelas. Genericity and existence of a minimum for scalar integrals functionals. J. Optim. Theory Appl. 86 (1995), 421-431.
    • (1995) J. Optim. Theory Appl. , vol.86 , pp. 421-431
    • Monteiro Marques, M.D.P.1    Ornelas, A.2
  • 21
    • 0003246772 scopus 로고
    • Multiple integrals in the calculus of variations
    • Springer
    • C. B. Morrey. Multiple integrals in the calculus of variations. Grundlehren Math. Wiss., vol. 130 (Springer, 1966).
    • (1966) Grundlehren Math. Wiss. , vol.130
    • Morrey, C.B.1
  • 22
    • 0001496391 scopus 로고
    • Calcul des variations et homogénéization
    • (ed. D. Bergman and others), Collect. Dir. Études Rech. Élec. France Paris
    • F. Murat and L. Tartar. Calcul des variations et homogénéization. In Les methodes de l'homogénéization: thèorie et applications en physique (ed. D. Bergman and others), vol. 57, pp. 316-369. Collect. Dir. Études Rech. Élec. France (Paris, 1985).
    • (1985) Les Methodes de l'Homogeńeízation: Thèorie et Applications en Physique , vol.57 , pp. 316-369
    • Murat, F.1    Tartar, L.2
  • 23
    • 0000640076 scopus 로고    scopus 로고
    • Existence of scalar minimizers for nonconvex simple integrals of sum type
    • A. Ornelas. Existence of scalar minimizers for nonconvex simple integrals of sum type. J. Math. Analysis Appl. 221 (1998), 559-573.
    • (1998) J. Math. Analysis Appl. , vol.221 , pp. 559-573
    • Ornelas, A.1
  • 24
    • 0011207047 scopus 로고
    • Existence of minimizers for vector problems without quasiconvexity condition
    • J. P. Raymond. Existence of minimizers for vector problems without quasiconvexity condition. Nonlinear Analysis 18 (1992), 815-825.
    • (1992) Nonlinear Analysis , vol.18 , pp. 815-825
    • Raymond, J.P.1
  • 25
    • 0004267646 scopus 로고
    • Princeton, NJ: Princeton University Press
    • T. Rockafeller. Convex analysis (Princeton, NJ: Princeton University Press, 1972).
    • (1972) Convex Analysis
    • Rockafeller, T.1
  • 27
    • 0032398499 scopus 로고    scopus 로고
    • An existence result for a class of non convex problems of the calculus of variations
    • G. Treu. An existence result for a class of non convex problems of the calculus of variations. J. Convex Analysis 5 (1998), 31-44.
    • (1998) J. Convex Analysis , vol.5 , pp. 31-44
    • Treu, G.1


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