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 12 is considered.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 29, Proceedings of KROMSH, 2008.
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Orlov, I.V. Hilbert compacts, compact ellipsoids, and compact extrema. J Math Sci 164, 637–647 (2010). https://doi.org/10.1007/s10958-010-9766-7
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DOI: https://doi.org/10.1007/s10958-010-9766-7