Linear continuous functionals on the space $(BV)$ with weak topologies
نویسندگان
چکیده
منابع مشابه
Strictly Continuous Extension of Functionals with Linear Growth to the Space Bv
In this paper, we prove that the integral functional F [u] : BV( ; Rm) → R defined by F [u] := ∫ f (x, u(x),∇u(x)) dx + ∫ ∫ 1 0 f ∞ ( x, u (x), dDsu d|Dsu| (x) ) dθ d|Dsu|(x) is continuous over BV( ; Rm), with respect to the topology of area-strict convergence, a topology in which (W1,1 ∩ C∞)( ; Rm) is dense. This provides conclusive justification for the treatment of F as the natural extension...
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7"o(z) being employed in general to denote the total variation of the function z(t) on /. Thus metrised, (BV) is not a Banach space(2); but it is complete, separable, and boundedly compact. Although a linear space, it is not a "linear topological space" in the sense in which that term is sometimes used, for the topology introduced by the metric (1) is non-uniform. Indeed it is easily seen that ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1966
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1966-0193490-3