Sobolev spaces

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

Mathematical inequality in Sobolev space theory

inequality on Lp norm with weak derivatives

Domain in a Euclidean space whose boundary is sufficiently regular

theorem about inclusions between Sobolev spaces: if 1≤r≤s<∞ and 1/r − k/n = 1/s − l/n, then Wᵏʳ(ℝⁿ) ⊆ Wˡˢ(ℝⁿ)

Theorem in functional analysis

compact embedding theorem concerning Sobolev spaces