The structure of extremals of a class of second order variational problems
Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) no. 5, pp. 593-629. 
@article{AIHPC_1999__16_5_593_0,
     author = {Marcus, Moshe and Zaslavski, Alexander J.},
     title = {The structure of extremals of a class of second order variational problems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {593--629},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {5},
     year = {1999},
     mrnumber = {1712568},
     zbl = {0989.49003},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1999__16_5_593_0/}
}
TY  - JOUR
AU  - Marcus, Moshe
AU  - Zaslavski, Alexander J.
TI  - The structure of extremals of a class of second order variational problems
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1999
SP  - 593
EP  - 629
VL  - 16
IS  - 5
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1999__16_5_593_0/
LA  - en
ID  - AIHPC_1999__16_5_593_0
ER  - 
%0 Journal Article
%A Marcus, Moshe
%A Zaslavski, Alexander J.
%T The structure of extremals of a class of second order variational problems
%J Annales de l'I.H.P. Analyse non linéaire
%D 1999
%P 593-629
%V 16
%N 5
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1999__16_5_593_0/
%G en
%F AIHPC_1999__16_5_593_0
Marcus, Moshe; Zaslavski, Alexander J. The structure of extremals of a class of second order variational problems. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) no. 5, pp. 593-629. http://www.numdam.org/item/AIHPC_1999__16_5_593_0/

[1] R.A. Adams, Sobolev spaces, Academic Press, New York, 1975. | MR | Zbl

[2] J.P. Aubin and I. Ekeland, Applied nonlinear analysis, Wiley-Interscience, New York, 1984. | MR | Zbl

[3] L.D. Berkovitz, Lower semicontinuity of integral functionals, Trans. Amer. Math. Soc., Vol. 192, 1974, pp. 51-57. | MR | Zbl

[4] D.A. Carlson, The existence of catching-up optimal solutions for a class of infinite horizon optimal control problems with time delay, SIAM Journal on Control and Optimization, Vol. 28 , 1990, pp. 402-422. | MR | Zbl

[5] D.A. Carlson, A. Jabrane and A. Haurie, Existence of overtaking solutions to infinite dimensional control problems on unbounded time intervals, SIAM Journal on Control and Optimization, Vol. 25, 1987 , pp. 1517-1541. | MR | Zbl

[6] D.A. Carlson, A. Haurie and A. Leizarowitz, Infinite horizon optimal control, Springer-Verlag, Berlin, 1991. | MR | Zbl

[7] B.D. Coleman, M. Marcus and V.J. Mizel, On the thermodynamics of periodic phases, Arch. Rational Mech. Anal., Vol. 117, 1992, pp. 321-347. | MR | Zbl

[8] J.L. Kelley, General topology, Van Nostrand , Princeton, NJ, 1955. | MR | Zbl

[9] A. Leizarowitz, Infinite horizon autonomous systems with unbounded cost, Appl. Math. Optim., Vol. 13, 1985 , pp. 19-43. | MR | Zbl

[10] A. Leizarowitz and V.J. Mizel, One dimensional infinite horizon variational problems arising in continuum mechanics , Arch. Rational Mech. Anal., Vol. 106, 1989, pp. 161- 194. | MR | Zbl

[11] V.L. Makarov and A.M. Rubinov, Mathematical theory of econimic dynamics and equilibria, Springer -Verlag, New York, 1977. | MR | Zbl

[12] M. Marcus, Uniform estimates for a variational problem with small parameters, Arch. Rational Mech. Anal., Vol. 124, 1993 , pp. 67-98. | MR | Zbl

[13] M. Marcus, Universal properties of stable states of a free energy model with small parameters, Cal. Var. , to appear. | MR | Zbl

[14] V.J. Mizel, L.A. Peletier and W.C. Troy , Periodic phases in second order materials, Preprint, 1997. | MR

[15] A.J. Zaslavski, The existence of periodic minimal energy configurations for one-dimensional infinite horizon variational problems arising, in continuum mechanics, J. Math. Anal. Appl., Vol. 194, 1995, pp. 459-476. | MR | Zbl

[16] A.J. Zaslavski, The existence and structure of extremals for a class of second order infinite horizon variational problems, J. Math. Anal. Appl., Vol. 194, 1995, pp. 660-696. | MR | Zbl

[17] A.J. Zaslavski, Structure of extremals for one-dimensional variational problems arising in continuum mechanics , J. Math. Anal. Appl., Vol. 198, 1996, pp. 893-921. | MR | Zbl

[18] A.J. Zaslavski , The asymptotic turnpike property and the uniqueness of a periodic minimal solution for one-dimensional variational problems, Preprint, 1996. | MR