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A formula for the functions realizing functionals. (Russian, English) Zbl 0986.46020
Sib. Mat. Zh. 42, No. 4, 920-925 (2001); translation in Sib. Math. J. 42, No. 4, 774-778 (2001).
Using results of his previous article [Sib. Math. J. 38, No. 1, 140–146 (1997; Zbl 0868.46022)], the author proves the formula \[ u(x)=(-1)^m\lim_{\varepsilon\to 0}\int\limits_{E_n} \sum\limits_{|\alpha|=m}K_\alpha (x,y)(l\circ G_{\varepsilon}^{(\alpha)})(y) dy \] for the functions \(u\) realizing functionals \(l\) in Sobolev spaces.
MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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