This article is cited in 7 papers

Hilbert compacts, compact ellipsoids, and compact extrema

I. V. Orlov

Vernadskiy Tavricheskiy National University

Abstract: 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.

UDC: 517.98

 English version: Journal of Mathematical Sciences, 2010, 164:4, 637–647

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