##  [Sobolev Embedding](/sobolev-embedding) 

  ##  [Sobolev Embedding](https://puremath.quantumdictionary.io/sobolev-embedding-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A family of results that identify when a Sobolev space W^{k,p}(Ω) (or its fractional variants) is continuously or compactly included in a Lebesgue space L^q(Ω), a Hölder space C^{0,α}(Ω), or another Sobolev space; the statements specify relations between derivative order, integrability exponent, and the spatial dimension or regularity of Ω.