Lavrentiev's phenomenon for totally unconstrained variational problems in one dimension

Nonlinear Differential Equations and Applications

Volumn 7, Issue 4, 2000, Pages 435-446

  Dani, Keshav ^a   Hrusa, William J ^a   Mizel, Victor J ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038697574     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001434     Document Type: Article

References (20)

1. G. ALBERTI, P. MAJER, Gap phenomenon for some autonomous functionals, J. Conv. Anal. 1 (1994), 31-45.
2. G. ALBERTI, F. SERRA CASSANO, Nonoccurrence of gap for one-dimensional autonomous functionals, preprint, Istituto di Matematiche Applicate, Universitá di Pisa 1994.
3. T.S. ANGELL, A note on the approximation of optimal solutions of the calculus of variations, Rend. Circ. Mat. Palermo 2 (1979), 258-278.
4. J.M. BALL, V.J. MIZEL, One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equations, Arch Rational Mech. Anal. 90 (1985), 325-388.
5. G. BUTTAZZO, The gap phenomenon for integral functionals: results and open questions, Proceedings of Variational Methods, Nonlinear Analysis and Differential Equations, Genova 27-30 September, 1993, ECIG, Geneva, 1994, 59-59.
6. G. BUTTAZZO, M. BELLONI, A survey on old and recent results about the gap phenomenon, in: Recent Developments in Well-Posed Variational Problems, ed. by R. Lucchetti and J. Revalski, Kluwer Academic Publishers, Dordrecht (1995), 1-27.
7. L. CESARI, Optimization-Theory and Applications, Springer-Verlag, Berlin, 1983.
8. F.H. CLARKE, R.B. VINTER, Regularity properties of solutions to the basic problem in the calculus of variations, Trans. Amer. Math. Soc. 291 (1985), 73-98.
9. A.M. DAVIE, Singular minimizers in the calculus of variations in one dimension, Arch. Rational Mech. Anal. 101 (1988), 161-177.
10. A.C. HEINRICHER, V.J. MIZEL, The Lavrentiev phenomenon for invariant variational problems, Arch, Rational Mech. Anal. 102 (1988), 57-93.
11. A.C. HEINRICHER, V.J. MIZEL, A new example of the Lavrentiev phenomenon, SIAM J. Control Optim. 26 (1988), 1490-1503.
12. W.J. HRUSA, Lavrentiev's phenomenon for second-order autonomous variational problems in one dimension, preprint.
13. M. LAVRENTIEV, Sur quelques problèmes du calcul des variations, Ann. Mat. Pura Appl. 4 (1926), 107-124.
14. P.D. LOEWEN, On the Lavrentiev phenomenon, Can. Math. Bull. 30 (1987), 102-108.
15. B. MANIÀ, Sopra un esempio di Lavrentiev, Boll. Un. Mat. Ital. 13 (1934), 146-153.
16. M.A. SYCHEV, On the regularity of solutions of some variational problems, Sov. Math. Dokl. 43 (1991), 292-296.
17. M.A. SYCHEV, On a classical problem of the calculus of variations, Sov. Math. Dokl. 44 (1992), 116-120.
18. L. TONELLI, Fondamenti di Calcolo delle Variazioni, Zanichelli, Vols. I, II, 1921-1923.
19. L. TONELLI, Sulle estremaloidi del Calcolo della variazioni, Rend. R. Accad. Lincei 21 (1935), 289-293 (in L.'Tonelli, Opere Scelle Vol. Ill, #107 Edizioni Cremonese, Roma, 1961).
20. L. TONELLI, Sugli integrali del calcolo delle variazioni in forma ordinaria, Ann. R. Scuola Norm. Sup. Pisa 3 (1934), 401-450 (in L. Tonelli Opere Scelte Vol. Ill #105, Edizioni Cremonese, Roma, 1961).