Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
calculus of variations
approximation theory theory of partial differential equations |
| gptkbp:contains |
functions with weak derivatives
|
| gptkbp:defines |
vector space of functions equipped with a norm that involves both the function and its derivatives
|
| gptkbp:field |
gptkb:mathematics
functional analysis partial differential equations |
| gptkbp:generalizes |
space of differentiable functions
|
| gptkbp:hasSpecialCase |
gptkb:L^p_space
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sobolev space
|
| gptkbp:introducedIn |
1930s
|
| gptkbp:namedAfter |
gptkb:Sergei_Sobolev
|
| gptkbp:notation |
W^{k,p}(Ω)
|
| gptkbp:property |
gptkb:Hilbert_space
gptkb:Hilbert_space_(for_p=2) |
| gptkbp:relatedTo |
gptkb:Poincaré_inequality
gptkb:Rellich–Kondrachov_theorem gptkb:Sobolev_inequality distribution (mathematics) embedding theorem trace theorem weak derivative |
| gptkbp:usedIn |
finite element method
regularity theory variational methods |
| gptkbp:bfsParent |
gptkb:L^p_space
|
| gptkbp:bfsLayer |
5
|