Statements (39)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
function space
|
| gptkbp:application |
gptkb:elasticity_theory
gptkb:signal_processing fluid dynamics quantum mechanics finite element method image processing |
| gptkbp:basisFor |
calculus of variations
regularity theory modern PDE theory |
| gptkbp:characterizedBy |
integrability
weak derivatives |
| gptkbp:contains |
functions with weak derivatives up to order k in L^p
|
| gptkbp:definedIn |
open subsets of R^n
|
| gptkbp:field |
gptkb:mathematics
functional analysis partial differential equations |
| gptkbp:generalizes |
gptkb:Lp_spaces
classical differentiable functions |
| gptkbp:hasSpecialCase |
H^1 is W^{1,2}
H^k is W^{k,2} |
| https://www.w3.org/2000/01/rdf-schema#label |
Sobolev spaces
|
| gptkbp:importantFor |
compactness
density of smooth functions embedding theorems trace theorems |
| gptkbp:introducedIn |
1930s
|
| gptkbp:namedAfter |
gptkb:Sergei_Sobolev
|
| gptkbp:notation |
H^k
W^{k,p} |
| gptkbp:relatedTo |
gptkb:Banach_spaces
gptkb:Hilbert_spaces Fourier analysis distribution theory |
| gptkbp:usedIn |
approximation theory
variational calculus theory of partial differential equations |
| gptkbp:bfsParent |
gptkb:Sergey_Sobolev
|
| gptkbp:bfsLayer |
5
|