Geodesic
On a~minimum in variational elliptic problems without convexity assumptions
Matematičeskie zametki, Tome 65 (1999) no. 1, pp. 130-142.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{MZM_1999_65_1_a12,
     author = {D. A. Tolstonogov},
     title = {On a~minimum in variational elliptic problems without convexity assumptions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {130--142},
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1999_65_1_a12/}
}
TY  - JOUR
AU  - D. A. Tolstonogov
TI  - On a~minimum in variational elliptic problems without convexity assumptions
JO  - Matematičeskie zametki
PY  - 1999
SP  - 130
EP  - 142
VL  - 65
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1999_65_1_a12/
LA  - ru
ID  - MZM_1999_65_1_a12
ER  - 
%0 Journal Article
%A D. A. Tolstonogov
%T On a~minimum in variational elliptic problems without convexity assumptions
%J Matematičeskie zametki
%D 1999
%P 130-142
%V 65
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1999_65_1_a12/
%G ru
%F MZM_1999_65_1_a12
D. A. Tolstonogov. On a~minimum in variational elliptic problems without convexity assumptions. Matematičeskie zametki, Tome 65 (1999) no. 1, pp. 130-142. http://geodesic.mathdoc.fr/item/MZM_1999_65_1_a12/

[1] Ekland I., Temam R., Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979

[2] Sychev M. A., “Neobkhodimye i dostatochnye usloviya v teoremakh polunepreryvnosti i skhodimosti s funktsionalom”, Matem. sb., 186:6 (1995), 77–108 | MR | Zbl

[3] Cellina A., Colombo G., “On a classical problem of the calculus of variations without convexity assumptions”, Ann. Inst. H. Poincaré. Anal. Non Linéaire, 7:2 (1990), 97–106 | MR | Zbl

[4] Raymond J. P., “Existence theorems in optimal control problems without convexity assumptions”, J. Optim. Theory Appl., 67 (1990), 109–132 | DOI | MR | Zbl

[5] Mariconda C., “A generalization of the Cellina–Colombo theorem for a class of nonconvex variational problems”, J. Math. Anal. Appl., 1975 (1993), 514–522 | DOI | MR

[6] Colombo G., Goncharov V. V., “Existence for a nonconvex optimal control problem with nonlinear dynamics”, Nonlinear Anal., 24:6 (1995), 795–800 | DOI | MR | Zbl

[7] Colombo G., Goncharov V. V., “On a class of nonconvex and nonlinear optimal control problems”, Nonlinear Differential Equations Appl. (NoDEA), 3 (1996), 115–126 | DOI | MR

[8] Olech C., “Integrals of set-valued functions and linear optimal control problems”, Colloque sur la Théorie Mathématique du Controle Optimal, CBRM (Vander Louvain, 1970), 109–125

[9] Chesari L., Optimization Theory and Applications, Springer, New York, 1983

[10] Cellina A., “On minima of a functional of the gradient: sufficient conditions”, Nonlinear Anal., 20 (1993), 343–347 | DOI | MR | Zbl

[11] Cellina A., Perrotta S., “On minima of radially symmetric functionals of the gradient”, Nonlinear Anal., 23 (1994), 239–249 | DOI | MR | Zbl

[12] Flores F., On Radial Solutions to Non-Convex Variational Problems, Preprint SISSA, Ref. 127/M, 1991

[13] Cellina A., Minimizing a Functional Depending on $\nabla u$ and on $u$, Preprint SISSA, Ref. 41/95/M, 1995

[14] Balder E., “New existence results for optimal control in the absence of convexity: the importance of extremality”, SIAM J. Control Optim., 32:3 (1994), 890–916 | DOI | MR | Zbl

[15] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972

[16] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | Zbl

[17] Shvarts L., Analiz, T. 1, Mir, M., 1972

[18] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | Zbl