Geodesic
Conditions on Determining Functionals for Subsets of Sobolev Space
Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 892-902.

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

We study conditions for the set of determining functionals and apply the obtained results to studying the uniqueness of the solution of the Dirichlet problem for elliptic equations of second order.
Keywords: elliptic equation of second order, Dirichlet problem, determining functional, linear continuous functional, Sobolev space
Mots-clés : Sturm–Liouville problem, Fourier coefficient. 
@article{MZM_2009_86_6_a7,
     author = {T. Yu. Semenova},
     title = {Conditions on {Determining} {Functionals} for {Subsets} of {Sobolev} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {892--902},
     publisher = {mathdoc},
     volume = {86},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a7/}
}
TY  - JOUR
AU  - T. Yu. Semenova
TI  - Conditions on Determining Functionals for Subsets of Sobolev Space
JO  - Matematičeskie zametki
PY  - 2009
SP  - 892
EP  - 902
VL  - 86
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a7/
LA  - ru
ID  - MZM_2009_86_6_a7
ER  - 
%0 Journal Article
%A T. Yu. Semenova
%T Conditions on Determining Functionals for Subsets of Sobolev Space
%J Matematičeskie zametki
%D 2009
%P 892-902
%V 86
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a7/
%G ru
%F MZM_2009_86_6_a7
T. Yu. Semenova. Conditions on Determining Functionals for Subsets of Sobolev Space. Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 892-902. http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a7/

[1] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR | Zbl

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

[3] I. D. Chueshov, “Zamechanie o mnozhestvakh opredelyayuschikh elementov dlya sistem reaktsii-diffuzii”, Matem. zametki, 63:5 (1998), 774–784 | MR | Zbl

[4] I. D. Chueshov, “Teoriya funktsionalov, odnoznachno opredelyayuschikh asimptoticheskuyu dinamiku beskonechnomernykh dissipativnykh sistem”, UMN, 53:4 (1998), 77–124 | MR | Zbl

[5] O. A. Ladyzhenskaya, “Ob otsenkakh fraktalnoi razmernosti i chisla opredelyayuschikh mod dlya invariantnykh mnozhestv dinamicheskikh sistem”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 19, Zap. nauchn. sem. LOMI, 163, Izd-vo «Nauka», Leningrad. otd., L., 1987, 105–129 | MR | Zbl

[6] D. A. Jones, E. S. Titi, “Upper bounds on the number of determining modes, nodes, and volume elements for the Navier–Stokes equations”, Indiana Univ. Math. J., 42:3 (1993), 875–887 | MR | Zbl

[7] D. A. Jones, E. S. Titi, “Determining finite volume elements for the 2D Navier–Stokes equations”, Phys. D., 60:1–4 (1992), 165–174 | DOI | MR | Zbl

[8] I. G. Tsarkov, “Ustoichivost odnoznachnoi razreshimosti v nekorrektnoi zadache Dirikhle”, Matem. zametki, 79:2 (2006), 294–308 | MR | Zbl

[9] T. Yu. Semenova, “Priblizhenie funktsii prostranstv Soboleva stupenchatymi funktsiyami i edinstvennost reshenii differentsialnykh uravnenii vida $u''=F(x,u,u')$”, Izv. RAN. Ser. matem., 71:1 (2007), 155–186 | MR | Zbl

[10] T. Yu. Semenova, “Ob odnom klasse opredelyayuschikh funktsionalov dlya kvazilineinykh ellipticheskikh zadach”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2009, no. 1, 11–15 | MR

[11] S. I. Pokhozhaev, “Nonlinear variational problems via the fibering method”, Handbook of Differential Equations: Stationary Partial Differential Equations, Vol. V, Handb. Differ. Equ., Elsevier, Amsterdam, 2008, 49–209 | MR

[12] L. Nirenberg, Lektsii po nelineinomu funktsionalnomu analizu, Matematika. Novoe v zarubezhnoi nauke, 5, Mir, M., 1977 | MR | Zbl