# zbMATH — the first resource for mathematics

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:
 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 4.6e+31 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Full Text: