Geodesic
Generalized Admissibility, Well-Definedness, and Invertibility of Linear Partial Differential Operators
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 343-346.

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It is shown that the concepts of generalized admissibility (Massera) and well-definedness (Zhikov) for linear partial differential operators on $\mathbb R^n$ are equivalent in the Hilbert space. Applications are considered. 
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     author = {V. M. Tyurin},
     title = {Generalized {Admissibility,} {Well-Definedness,} and {Invertibility} of {Linear} {Partial} {Differential} {Operators}},
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V. M. Tyurin. Generalized Admissibility, Well-Definedness, and Invertibility of Linear Partial Differential Operators. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 343-346. http://geodesic.mathdoc.fr/item/TM_2002_236_a35/

[1] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, 3-e izd., pererabot. i dop., Nauka, M., 1988 | MR

[2] Teilor M., Psevdodifferentsialnye operatory, Mir, M., 1985 | MR

[3] Massera Kh., Sheffer Kh., Lineinye differentsialnye uravneniya i funktsionalnye prostranstva, Mir, M., 1970 | MR | Zbl

[4] Zhikov V. V., “Nekotorye voprosy dopustimosti i dikhotomii. Printsip usredneniya”, Izv. AN SSSR, 40:6 (1976), 1380–1480 | MR

[5] Levitan B. M., Zhikov V. V., Pochti periodicheskie funktsii i differentsialnye uravneniya, MGU, M., 1978 | MR

[6] Tyurin V. M., “O nekotorykh koertsitivnykh neravenstvakh dlya lineinykh differentsialnykh operatorov s chastnymi proizvodnymi”, Sib. mat. zhurn., 39:3 (1998), 650–659 | MR | Zbl