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Clear filtersDeGiorgi.memW01p_of_contDiff_hasCompactSupport
Plain-language statement
A smooth compactly supported function belongs to W₀^{1,p}(ℝ^d).
Source project: DeGiorgi
Person-level attribution pending.
DeGiorgi.memW01p_of_contDiff_hasCompactSupport_subset
Plain-language statement
A smooth compactly supported function whose support is contained in an open set belongs to W₀^{1,p} on that set.
Source project: DeGiorgi
Person-level attribution pending.
DeGiorgi.memW01p_of_memW1p_of_tsupport_subset
Plain-language statement
Localization by compact support: a finite-p Sobolev function whose support is compactly contained in an open set belongs to W₀^{1,p}.
Source project: DeGiorgi
Person-level attribution pending.
DeGiorgi.MemW01p.add
Plain-language statement
H₀¹(Ω) is closed under addition.
Source project: DeGiorgi
Person-level attribution pending.
DeGiorgi.MemW01p.smul
Plain-language statement
H₀¹(Ω) is closed under scalar multiplication.
Source project: DeGiorgi
Person-level attribution pending.
DeGiorgi.MemW1pWitness.ae_eq
Plain-language statement
Two W^{1,2} witnesses on an open set have a.e.-equal gradients.
Source project: DeGiorgi
Person-level attribution pending.