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. 
@article{TM_2002_236_a35,
     author = {V. M. Tyurin},
     title = {Generalized {Admissibility,} {Well-Definedness,} and {Invertibility} of {Linear} {Partial} {Differential} {Operators}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {343--346},
     publisher = {mathdoc},
     volume = {236},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a35/}
}
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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/