Compact embedding is a concept from functional analysis, particularly within the context of Sobolev spaces and other function spaces. It describes a situation where one function space can be embedded into another in such a way that bounded sets in the first space are mapped to relatively compact sets in the second space.
Articles by others on the same topic
A compact embedding of Banach spaces is an injective continuous linear map that sends every bounded set to a relatively compact subset. Equivalently, every bounded sequence in has a subsequence converging in . One identifies with its image when is the natural inclusion. The Rellich-Kondrachov theorem supplies many compact embeddings between Sobolev spaces and Lp spaces on bounded domains.