On non-Archimedean quantitative compactness theorems

2016 ◽  
pp. 91-102
Author(s):  
J. Kakol ◽  
A. Kubzdela
Keyword(s):  
Compactness Theorems

scholarly journals Compactness theorems for problems with unknown boundary

2021 ◽  
Vol 21 (1) ◽  
pp. 105-112
Author(s):  
A.G. Podgaev ◽  
◽  
T.D. Kulesh ◽  
Keyword(s):  
Phase Transitions ◽  
Approximate Solutions ◽  
Compactness Theorem ◽  
Unknown Boundary ◽  
Entire Domain ◽  
Higher Derivatives ◽  
Compactness Theorems

The compactness theorem is proved for sequences of functions that have estimates of the higher derivatives in each subdomain of the domain of definition, divided into parts by a sequence of some curves of class W_2^1. At the same time, in the entire domain of determining summable higher derivatives, these sequences do not have. These results allow us to make limit transitions using approximate solutions in problems with an unknown boundary that describe the processes of phase transitions.

A Compact Imbedding Theorem for Functions without Compact Support

1971 ◽  
Vol 14 (3) ◽  
pp. 305-309 ◽  
Author(s):  
R. A. Adams ◽  
John Fournier
Keyword(s):  
Sobolev Space ◽  
Compact Support ◽  
Unbounded Domains ◽  
Bounded Domains ◽  
Complete Continuity ◽  
Compact Imbedding ◽  
Compactness Theorems ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Made In

The extension of the Rellich-Kondrachov theorem on the complete continuity of Sobolev space imbeddings of the sort1to unbounded domains G has recently been under study [1–5] and this study has yielded [4] a condition on G which is necessary and sufficient for the compactness of (1). Similar compactness theorems for the imbeddings2are well known for bounded domains G with suitably regular boundaries, and the question naturally arises whether any extensions to unbounded domains can be made in this case.

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