Geodesic
Hilbert compacts, compact ellipsoids, and compact extrema
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 29 (2008), pp. 165-175.

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We consider a system of so-called Hilbert compacts $K(H)$ in a Hilbert space $H$; those Hilbert compacts admit a two-sided estimate by compact ellipsoids in $H$. For functionals in $H$, we introduce the notion of a compact extremum achieved at a certain base with respect to the imbedding in $K(H)$. An example of the $K$-extremum of a variational functional in the Sobolev space $W_2^1$ is considered. 
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I. V. Orlov. Hilbert compacts, compact ellipsoids, and compact extrema. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 29 (2008), pp. 165-175. http://geodesic.mathdoc.fr/item/CMFD_2008_29_a8/

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