Geodesic
On $(p,l)$-capacity, inbedding theorems, and the spectrum of a~selfadjoint elliptic operator
Izvestiya. Mathematics , Tome 7 (1973) no. 2, pp. 357-387

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Necessary and sufficient conditions are found for continuity, compactness, and closability of imbedding operators of some function spaces into the space $L_p$. These results (for $p=2$) give criteria for positive definiteness and discreteness of the spectrum of the Dirichlet problem for a selfadjoint elliptic operator of arbitrary order. Some integral inequalities are considered for differentiable functions on a cube. 
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     author = {V. G. Maz'ya},
     title = {On $(p,l)$-capacity, inbedding theorems, and the spectrum of a~selfadjoint elliptic operator},
     journal = {Izvestiya. Mathematics },
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     volume = {7},
     number = {2},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a7/}
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V. G. Maz'ya. On $(p,l)$-capacity, inbedding theorems, and the spectrum of a~selfadjoint elliptic operator. Izvestiya. Mathematics , Tome 7 (1973) no. 2, pp. 357-387. http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a7/