Sobolev Spaces
This category covers Sobolev spaces $W^{m,p}$.
Sobolev spaces are generalizations of $L^{p}$ spaces. In simple terms, they are spaces of functions whose derivatives up to order $m$ all belong to $L^{p}$.
Sobolev Spaces
- Sobolev Norms and Sobolev Spaces
- Sobolev Spaces Are Banach Spaces
- Sobolev Spaces Are Separable, Uniformly Convex, and Reflexive
Embedding Theorems
Various Definitions
- Finite Cone
- Locally Finite
- Cone Condition
- Weak Cone Condition
- Segment Condition
- Uniform Cone Condition
- Strong Local Lipschitz Condition
- Uniform $C^{m}$-Regularity Condition
References
- Robert A. Adams and John J. F. Foutnier, Sobolev Space (2nd Edition, 2003)
All posts
- Sobolev Norm and Sobolev Spaces
- Sobolev Spaces are Banach Spaces: A Proof
- Sobolev Spaces are Separable, Uniformly Convex, and Reflexive: A Proof
- Finite Cone
- Locally Finite Covers
- Under Cone Conditions
- Weak Cone Condition
- Line Segment Conditions
- Uniform Cone Condition
- Strong Local Lipschitz Condition
- Uniform C^m-Regularity Condition