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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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calculus of variations
approximation theory
theory of partial differential equations
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gptkbp:contains
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functions with weak derivatives
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gptkbp:defines
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vector space of functions equipped with a norm that involves both the function and its derivatives
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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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space of differentiable functions
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gptkbp:hasSpecialCase
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gptkb:L^p_space
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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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W^{k,p}(Ω)
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gptkbp:property
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gptkb:Hilbert_space
gptkb:Hilbert_space_(for_p=2)
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gptkbp:relatedTo
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gptkb:Poincaré_inequality
gptkb:Rellich–Kondrachov_theorem
gptkb:Sobolev_inequality
distribution (mathematics)
embedding theorem
trace theorem
weak derivative
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gptkbp:usedIn
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finite element method
regularity theory
variational methods
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gptkbp:bfsParent
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gptkb:Hardy_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 space
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