메뉴 건너뛰기




Volumn 131, Issue 1, 2001, Pages 155-184

Sufficiency theorems for local minimizers of the multiple integrals of the calculus of variations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0001118975     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500000822     Document Type: Article
Times cited : (15)

References (36)
  • 2
    • 0017417265 scopus 로고
    • Convexity conditions and existence theorems in elasticity
    • J. M. Ball. Convexity conditions and existence theorems in elasticity. Arch. Ration. Mech. Analysis 63 (1977), 337-403.
    • (1977) Arch. Ration. Mech. Analysis , vol.63 , pp. 337-403
    • Ball, J.M.1
  • 3
    • 0021296252 scopus 로고
    • Quasiconvexity at the boundary, positivity of the second variation and elastic stability
    • J. M. Ball and J. E. Marsden. Quasiconvexity at the boundary, positivity of the second variation and elastic stability. Arch. Ration. Mech. Analysis 86 (1984), 251-277.
    • (1984) Arch. Ration. Mech. Analysis , vol.86 , pp. 251-277
    • Ball, J.M.1    Marsden, J.E.2
  • 4
    • 0009238688 scopus 로고
    • Remarks on rank-one convexity and quasiconvexity
    • Harlow: Longman
    • J. M. Ball and F. Murat. Remarks on rank-one convexity and quasiconvexity. Pitman Research Notes Mathematics Series, no. 254 (Harlow: Longman, 1991)
    • (1991) Pitman Research Notes Mathematics Series , Issue.254
    • Ball, J.M.1    Murat, F.2
  • 5
    • 0000966233 scopus 로고
    • Null-Lagrangians, weak continuity and variational problems of arbitrary order
    • J. M. Ball, J. C. Currie and P. J. Olver. Null-Lagrangians, weak continuity and variational problems of arbitrary order. J. Funct. Analysis 41 (1981), 135-174.
    • (1981) J. Funct. Analysis , vol.41 , pp. 135-174
    • Ball, J.M.1    Currie, J.C.2    Olver, P.J.3
  • 15
    • 84972453494 scopus 로고
    • The Weierstrass condition for multiple integral variational problems
    • L. M. Graves. The Weierstrass condition for multiple integral variational problems. Duke Math. J. 5 (1939), 656-660.
    • (1939) Duke Math. J. , vol.5 , pp. 656-660
    • Graves, L.M.1
  • 17
    • 11744270925 scopus 로고
    • Sufficient conditions for multiple integral problems in the calculus of variations
    • M. R. Hestenes. Sufficient conditions for multiple integral problems in the calculus of variations. Am. J. Math. 70 (1968), 239-276.
    • (1968) Am. J. Math. , vol.70 , pp. 239-276
    • Hestenes, M.R.1
  • 19
    • 84972318821 scopus 로고
    • Weierstrass condition for the general basic variational problem
    • F. Hüsseinov. Weierstrass condition for the general basic variational problem. Proc. R. Soc. Edinb. A 125 (1995), 801-806.
    • (1995) Proc. R. Soc. Edinb. A , vol.125 , pp. 801-806
    • Hüsseinov, F.1
  • 20
    • 33747060063 scopus 로고
    • Sui criterii sufficienti per il massimo e per il minimo nel calcolo delle variazioni
    • E. E. Levi. Sui criterii sufficienti per il massimo e per il minimo nel calcolo delle variazioni. Annali Mat. Pura Appl. 21 (1913), 173-218.
    • (1913) Annali Mat. Pura Appl. , vol.21 , pp. 173-218
    • Levi, E.E.1
  • 21
    • 84968503702 scopus 로고
    • Quasiconvexity and lower semicontinuity of multiple integrals of any order
    • N. G. Meyers. Quasiconvexity and lower semicontinuity of multiple integrals of any order. Trans. Am. Math. Soc. 119 (1965), 225-249.
    • (1965) Trans. Am. Math. Soc. , vol.119 , pp. 225-249
    • Meyers, N.G.1
  • 22
    • 84972497511 scopus 로고
    • Quasiconvexity and lower semicontinuity of multiple integrals
    • C. B. Morrey. Quasiconvexity and lower semicontinuity of multiple integrals. Pacific J. Math. 2 (1952), 25-53.
    • (1952) Pacific J. Math. , vol.2 , pp. 25-53
    • Morrey, C.B.1
  • 24
    • 33747049155 scopus 로고
    • Sufficient conditions by expansion methods for the problem of Bolza in the calculus of variations
    • W. T. Reid. Sufficient conditions by expansion methods for the problem of Bolza in the calculus of variations. Ann. Math. 38 (1937), 662-678.
    • (1937) Ann. Math. , vol.38 , pp. 662-678
    • Reid, W.T.1
  • 26
    • 0002483769 scopus 로고
    • On the positivity of the second variation in finite elasticity
    • H. C. Simpson and S. J. Spector. On the positivity of the second variation in finite elasticity. Arch. Ration. Mech. Analysis 98 (1987), 1-30.
    • (1987) Arch. Ration. Mech. Analysis , vol.98 , pp. 1-30
    • Simpson, H.C.1    Spector, S.J.2
  • 27
    • 33747043248 scopus 로고
    • Necessary conditions at the boundary for minimizers in finite elasticity
    • H. C. Simpson and S. J. Spector. Necessary conditions at the boundary for minimizers in finite elasticity. Arch. Ration. Mech. Analysis 107 (1989), 347-369.
    • (1989) Arch. Ration. Mech. Analysis , vol.107 , pp. 347-369
    • Simpson, H.C.1    Spector, S.J.2
  • 29
    • 0012944866 scopus 로고
    • The generalized Hamilton-Jacobi inequality and the stability of equilibria in non-linear elasticity
    • J. Sivaloganathan. The generalized Hamilton-Jacobi inequality and the stability of equilibria in non-linear elasticity. Arch. Ration. Mech. Analysis 107 (1989), 105-125.
    • (1989) Arch. Ration. Mech. Analysis , vol.107 , pp. 105-125
    • Sivaloganathan, J.1
  • 32
    • 0002185546 scopus 로고
    • Sur l'extension de la condition de Legendre du calcul des variations aux intégrales à plusieurs inconnues
    • L. van Hove. Sur l'extension de la condition de Legendre du calcul des variations aux intégrales à plusieurs inconnues. Proc. Koninklijke Nederlandsche Akademie Van Wetenschappen 50 (1947), 18-23.
    • (1947) Proc. Koninklijke Nederlandsche Akademie Van Wetenschappen , vol.50 , pp. 18-23
    • Van Hove, L.1
  • 34
    • 2542439880 scopus 로고
    • Polyconvexity and stability of equilibria in non-linear elasticity
    • K. Zhang. Polyconvexity and stability of equilibria in non-linear elasticity. Q. J. Mech. Appl. Math. 43 (1990), 215-221.
    • (1990) Q. J. Mech. Appl. Math. , vol.43 , pp. 215-221
    • Zhang, K.1
  • 35
    • 0242342817 scopus 로고
    • Remarks on quasiconvexity and stability of equilibria for variational integrals
    • K. Zhang. Remarks on quasiconvexity and stability of equilibria for variational integrals. Proc. Am. Math. Soc. 114 (1992), 927-930.
    • (1992) Proc. Am. Math. Soc. , vol.114 , pp. 927-930
    • Zhang, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.