Approximation of Sobolev Mappings
نویسنده
چکیده
where 1 sp < co. This definition is far from being intrinsic. For an intrinsic definition of WrTp(Mm, N”) see [ 11. In this space, beside the standard topology induced by the norm (1. ]ll,p, we also have weak topology and weak convergence. Let fk, f E W’~p(Mm), where 1 < p < co. We say that fk converges to f in weak topology iff fk + f in Lp and the set (lIVfk[lp)k is bounded. Weak convergence is denoted by fk f. It is not difficult to prove that our definition is equivalent to the standard definition of weak convergence in Banach space. We aim to prove the following theorem.
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