Geodesic
An energy inequality and the overdeterminacy property of a system of eigenfunctions
Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 695-707

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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. 
@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},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1968},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a1/}
}
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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/