In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its...

analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving...

Euclidean vector spaces, examples of Hilbert spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized...

function to the boundary of its domain to "generalized" functions in a Sobolev space. This is particularly important for the study of partial differential...

In mathematics, the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality...

delta function defines a bounded linear functional. The Sobolev embedding theorem for Sobolev spaces on the real line R implies that any square-integrable...

Orlicz spaces are many of the most important Sobolev spaces. In addition, the Orlicz sequence spaces are examples of Orlicz spaces. These spaces are called...

differential equations. Sobolev introduced notions that are now fundamental for several areas of mathematics. Sobolev spaces can be defined by some growth...

interpolation space is a space which lies "in between" two other Banach spaces. The main applications are in Sobolev spaces, where spaces of functions...

spaces, serve to generalize more elementary function spaces such as Sobolev spaces and are effective at measuring regularity properties of functions. Several...