Embeddings of anisotropic sobolev spaces
β Scribed by D. E. Edmunds; R. M. Edmunds
- Publisher
- Springer
- Year
- 1986
- Tongue
- English
- Weight
- 341 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0003-9527
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## Abstract Let Ξ© be an open subset of β^__n__^ and let __p__ β [1, __n__). We prove that the measure of nonβcompactness of the Sobolev embedding __W__^__k,p__^~0~(Ξ©) β __L__^__p__\*^(Ξ©) is equal to its norm. This means that the entropy numbers of this embedding are constant and equal to the norm.
This paper deals with various aspects of the theory and implementation of finite element methods for elliptic boundary value problems whose variational formulation is posed on anisotropic Sobolev spaces. The theory is applied to the Onsager pancake equation which arises in the study of high speed ga