On the representation of strictly continuous linear functionals
نویسندگان
چکیده
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15 صفحه اولStrictly 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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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1981
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500006428