Embedding and compact embedding for weighted and abstract Sobolev spaces

2019 ◽  
Vol 303 (2) ◽  
pp. 519-568
Author(s):  
Seng-Kee Chua
Keyword(s):  
Sobolev Spaces ◽  
Compact Embedding

scholarly journals A compact embedding theorem for generalized Sobolev spaces

2013 ◽  
Vol 265 (1) ◽  
pp. 17-57 ◽  
Author(s):  
Seng-Kee Chua ◽  
Scott Rodney ◽  
Richard Wheeden
Keyword(s):  
Sobolev Spaces ◽  
Embedding Theorem ◽  
Compact Embedding ◽  
Generalized Sobolev Spaces

On a class of weighted Sobolev spaces and the minimization of quadratic forms

1978 ◽  
Vol 81 (1-2) ◽  
pp. 119-130
Author(s):  
Frans Penning ◽  
Niko Sauer
Keyword(s):  
Weight Function ◽  
Sobolev Spaces ◽  
Compact Support ◽  
Quadratic Forms ◽  
Weighted Sobolev Spaces ◽  
Weight Functions ◽  
Compact Embedding ◽  
Embedding Theorems ◽  
Smooth Functions ◽  
Square Integrability

SynopsisIn this paper a class of weighted Sobolev spaces defined in terms of square integrability of the gradient multiplied by a weight function, is studied. The domain of integration is either the spaceRnor a half-space ofRn. Conditions on the weight functions that will ensure density of classes of smooth functions or functions with compact support, and compact embedding theorems, are derived. Finally the results are applied to a class of isoperimetrical problems in the calculus of variations in which the domain of integration is unbounded.

scholarly journals Compact embedding theorems and a Lions' type Lemma for fractional Orlicz–Sobolev spaces

2021 ◽  
Vol 300 ◽  
pp. 487-512
Author(s):  
Edcarlos D. Silva ◽  
M.L. Carvalho ◽  
J.C. de Albuquerque ◽  
Sabri Bahrouni
Keyword(s):  
Sobolev Spaces ◽  
Compact Embedding ◽  
Embedding Theorems

scholarly journals Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Przemysław Górka ◽  
Tomasz Kostrzewa ◽  
Enrique G. Reyes
Keyword(s):  
String Theory ◽  
Sobolev Spaces ◽  
Compactness Theorem ◽  
Compact Embedding ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Embeddings ◽  
Compact Abelian Groups ◽  
Lca Groups ◽  
Derivatives Of

We continue our research on Sobolev spaces on locally compact abelian (LCA) groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology. In this paper, we focus on compact embedding results and we prove an analog for LCA groups of the classical Rellich lemma and of the Rellich-Kondrachov compactness theorem. Furthermore, we introduce Sobolev spaces on subsets of LCA groups and study its main properties, including the existence of compact embeddings intoLp-spaces.

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