Souček space


In mathematics, Souček spaces are generalizations of Sobolev spaces, named after the Czech mathematician Jiří Souček. One of their main advantages is that they offer a way to deal with the fact that the Sobolev space W1,1 is not a reflexive space; since W1,1 is not reflexive, it is not always true that a bounded sequence has a weakly convergent subsequence, which is a desideratum in many applications.

Definition

Let Ω be a bounded domain in n-dimensional Euclidean space with smooth boundary. The Souček space W1,μ is defined to be the space of all ordered pairs, whereu lies in the Lebesgue space L1;v is a regular Borel measure on the closure of Ω;

Properties