High Quality Content by WIKIPEDIA articles! Let ? be a bounded domain in n-dimensional Euclidean space with smooth boundary. The Sou?ek space W1,?(?; Rm) is defined to be the space of all ordered pairs (u, v), where * u lies in the Lebesgue space L1(?; Rm); * v (thought of as the gradient of u) is a regular Borel measure on the closure of ?; * there exists a sequence of functions uk in the Sobolev space W1,1(?; Rm) such that lim_{k to infty} u_{k} = u mbox{ in } L^{1} (Omega; mathbf{R}^{m}) and lim_{k to infty} nabla u_{k} = v weakly-? in the space of all Rmxn-valued regular Borel measures on the closure of ?.

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