Geodesic
An energy inequality and the overdeterminacy property of a system of eigenfunctions
Izvestiya. Mathematics, Tome 2 (1968) no. 4, pp. 695-707 
V. I. Plotnikov. An energy inequality and the overdeterminacy property of a system of eigenfunctions. Izvestiya. Mathematics, Tome 2 (1968) no. 4, pp. 695-707. http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a1/
@article{IM2_1968_2_4_a1,
     author = {V. I. Plotnikov},
     title = {An energy inequality and the overdeterminacy property of a system of eigenfunctions},
     journal = {Izvestiya. Mathematics},
     pages = {695--707},
     year = {1968},
     volume = {2},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a1/}
}
TY  - JOUR
AU  - V. I. Plotnikov
TI  - An energy inequality and the overdeterminacy property of a system of eigenfunctions
JO  - Izvestiya. Mathematics
PY  - 1968
SP  - 695
EP  - 707
VL  - 2
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a1/
LA  - en
ID  - IM2_1968_2_4_a1
ER  - 
%0 Journal Article
%A V. I. Plotnikov
%T An energy inequality and the overdeterminacy property of a system of eigenfunctions
%J Izvestiya. Mathematics
%D 1968
%P 695-707
%V 2
%N 4
%U http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a1/
%G en
%F IM2_1968_2_4_a1

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

In this article we prove an energy inequality for the third boundary value problem (the parabolic case) and certain completeness and closure properties of the system of eigenfunctions.

[1] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[2] Plotnikov V. I., “Teoremy edinstvennosti, suschestvovaniya i apriornye svoistva obobschennykh reshenii”, Dokl. AN SSSR, 165:1 (1965), 33–35 | MR | Zbl

[3] Smirnov V. I., Kurs vysshei matematiki, tom V, Fizmatgiz, M., 1960

[4] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, LGU, L., 1950