Sobolev

Results named in Tau Ceti's TauCeti.Analysis.Sobolev modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

The L² Leibniz estimate to No Poincaré inequality holds on…

• The L² Leibniz estimate
• The analytic content of the extension theorem
• The borderline Sobolev inequality on W^{1,n}_0(Ω)
• De Giorgi's isoperimetric inequality
• The divergence theorem on a half-space (TauCeti.setIntegral_normalHalfSpace_fderiv_apply)
• The du Bois-Reymond lemma for weak derivatives
• Extension theorem for bounded Lipschitz domains
• The fundamental theorem of calculus for a continuous representative
• The fundamental theorem of calculus for weak derivatives
• The fundamental theorem of calculus for weak derivatives on the line
• The Gagliardo--Nirenberg--Sobolev inequality on W^{1,p}(E)
• Green's second identity against a test function
• The interior Sobolev inequality
• Jensen's bound for the gradient of a mollification
• The local Morrey inequality
• Meyers–Serrin: H = W in W^{k,p}(Ω)
• The Morrey potential estimate for the mean
• Morrey's Dirichlet growth theorem
• Morrey's inequality
• No Poincaré inequality holds on the whole space

The one-dimensional Poincaré… to Trudinger's inequality on…

• The one-dimensional Poincaré inequality
• The Poincaré inequality on a ball
• The Poincaré–Wirtinger inequality on a ball
• The pointwise Morrey estimate
• Rellich–Kondrachov on bounded Lipschitz domains
• The Sobolev inequality on W^{1,p}_0 of a ball
• The supercritical Sobolev multiplication estimate
• Trudinger's inequality on W^{1,n}_0(Ω)

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