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Transactions of the American Mathematical Society
Volumn 356, Issue 1, 2004, Pages 415-426
The classical problem of the calculus of variations in the autonomous case: Relaxation and Lipschitzianity of solutions
Author keywords

Regularity of solutions; Relaxation
Indexed keywords

EID: 0742288932     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-03-03347-6     Document Type: Article
Times cited : (40)
References (10)
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    • Ambrosio, L.1    Ascenzi, O.2    Buttazzo, G.3
  • 2
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    • One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
    • [B:M]. MR 86k:49002
    • [B:M] J. Ball and J. V. Mizel, One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation, Arch. Rat. Mech. Anal. 90 (1985), 325-388. MR 86k:49002
    • (1985) Arch. Rat. Mech. Anal. , vol.90 , pp. 325-388
    • Ball, J.1    Mizel, J.V.2
  • 3
    • 0041351876 scopus 로고    scopus 로고
    • Reparametrizations and approximate values of integrals of the calculus of variations
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    • [C:F:M] A. Cellina, A. Ferriero, and E. M. Marchini, Reparametrizations and approximate values of integrals of the calculus of variations, J. Differential Equations, to appear.
    • J. Differential Equations
    • Cellina, A.1    Ferriero, A.2    Marchini, E.M.3
  • 4
    • 0030147296 scopus 로고    scopus 로고
    • On the minimum problem for a class of non-coercive functionals
    • [C:T:Z]. MR 97d:49003
    • [C:T:Z] A. Cellina, G. Treu, and S. Zagatti, On the minimum problem for a class of non-coercive functionals, J. Differential Equations 127 (1996), 225-262. MR 97d:49003
    • (1996) J. Differential Equations , vol.127 , pp. 225-262
    • Cellina, A.1    Treu, G.2    Zagatti, S.3
  • 6
    • 84966256938 scopus 로고
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    • [C:V] F. H. Clarke and R. B. Vinter, Regularity properties of solutions to the basic problem in the calculus of variations, Trans. Amer. Math. Soc. 289 (1985), 73-98. MR 86h:49020
    • (1985) Trans. Amer. Math. Soc. , vol.289 , pp. 73-98
    • Clarke, F.H.1    Vinter, R.B.2
  • 9
    • 0004267646 scopus 로고
    • [R], Princeton Univ. Press, Princeton. MR 43:445
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    • (1970) Convex Analysis
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  • 10
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    • A general chain rule for derivatives and the change of variable formula for the Lebesgue integral
    • [S:V]. MR 40:280
    • [S:V] J. Serrin and D. E. Varberg, A general chain rule for derivatives and the change of variable formula for the Lebesgue integral, Amer. Math. Monthly 76 (1969), 514-520. MR 40:280
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    • Serrin, J.1    Varberg, D.E.2

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