Category
page 1Sobolev spaces
Sobolev space
Banach space of functions equipped with a norm that is a combination of Lᵖ-norms of the function itself and its weak derivatives up to a given order
Poincaré inequality
Mathematical inequality in Sobolev space theory
Friedrichs' inequality
inequality on Lp norm with weak derivatives
Lipschitz domain
Domain in a Euclidean space whose boundary is sufficiently regular
Sobolev inequality
theorem about inclusions between Sobolev spaces: if 1≤r≤s<∞ and 1/r − k/n = 1/s − l/n, then Wᵏʳ(ℝⁿ) ⊆ Wˡˢ(ℝⁿ)
Korn's inequality
Theorem in functional analysis
Rellich–Kondrachov theorem
compact embedding theorem concerning Sobolev spaces