On a strong connectness of weighted Sobolev spaces and compactness of the sequences of its elements (in. (Russian) Zbl 1137.35313
The notion of the strong connectness of Sobolev spaces was determined by E. Ya. Khruslov [Mat. Sb., N. Ser. 106(148), 604-621 (1978; Zbl 0381.35032)]. This property plays an important role in the study of the convergence of variational problems solutions in perforated domains. In this paper the authors establish the conditions on a weighted function, which are ensured a certain compactness of the sequences of functions with different domains of definitions and the strong connectness of corresponding Sobolev spaces for some type of perforated domains.
Reviewer: Nikolai V. Krasnoschok (Donetsk)
MSC:
35B40 | Asymptotic behavior of solutions to PDEs |
35J60 | Nonlinear elliptic equations |
35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |