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gptkbp:instanceOf
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gptkb:function_space
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gptkbp:application
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gptkb:elasticity_theory
gptkb:signal_processing
fluid dynamics
quantum mechanics
finite element method
image processing
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gptkbp:basisFor
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calculus of variations
regularity theory
modern PDE theory
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gptkbp:characterizedBy
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integrability
weak derivatives
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gptkbp:contains
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functions with weak derivatives up to order k in L^p
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gptkbp:definedIn
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open subsets of R^n
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gptkbp:field
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gptkb:partial_differential_equations
gptkb:mathematics
functional analysis
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gptkbp:generalizes
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gptkb:Lp_spaces
classical differentiable functions
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gptkbp:hasSpecialCase
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H^1 is W^{1,2}
H^k is W^{k,2}
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gptkbp:importantFor
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compactness
density of smooth functions
embedding theorems
trace theorems
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gptkbp:introducedIn
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1930s
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gptkbp:namedAfter
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gptkb:Sergei_Sobolev
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gptkbp:notation
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H^k
W^{k,p}
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gptkbp:relatedTo
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gptkb:Banach_spaces
gptkb:Hilbert_spaces
Fourier analysis
distribution theory
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gptkbp:usedIn
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approximation theory
variational calculus
theory of partial differential equations
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gptkbp:bfsParent
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gptkb:Friedrichs_inequality
gptkb:Moser–Trudinger_inequality
gptkb:Poincaré_inequality
gptkb:Gagliardo–Nirenberg_interpolation_inequality
gptkb:Riesz_potential
gptkb:Sergey_Sobolev
gptkb:Agmon's_inequality
gptkb:Lp_spaces
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gptkbp:bfsLayer
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6
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https://www.w3.org/2000/01/rdf-schema#label
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Sobolev spaces
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