Sou ek Space
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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 Rm×n-valued regular Borel measures on the closu...
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 Rm×n-valued regular Borel measures on the closure of .
