Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:appliesTo |
functions with weak derivatives
|
| gptkbp:field |
gptkb:mathematics
functional analysis partial differential equations |
| gptkbp:firstPublished |
1938
|
| gptkbp:form |
||u||_{L^q} ≤ C||∇u||_{L^p} for suitable p, q, and C
|
| gptkbp:generalizes |
gptkb:Gagliardo–Nirenberg_inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sobolev inequality
|
| gptkbp:implies |
functions in Sobolev spaces have additional regularity
|
| gptkbp:importantFor |
existence of solutions to PDEs
|
| gptkbp:namedAfter |
gptkb:Sergei_Sobolev
|
| gptkbp:relatedTo |
gptkb:Sobolev_space
embedding theorem |
| gptkbp:state |
Certain Sobolev spaces are continuously embedded in Lebesgue spaces
|
| gptkbp:usedIn |
analysis of PDEs
|
| gptkbp:bfsParent |
gptkb:Poincaré_inequality
gptkb:Gagliardo–Nirenberg_interpolation_inequality gptkb:Lieb–Thirring_inequality gptkb:Sobolev_space gptkb:Sergei_Sobolev |
| gptkbp:bfsLayer |
6
|