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 W12 is considered.
Citation:
I. V. Orlov, “Hilbert compacts, compact ellipsoids, and compact extrema”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 29, PFUR, M., 2008, 165–175; Journal of Mathematical Sciences, 164:4 (2010), 637–647
\Bibitem{Orl08}
\by I.~V.~Orlov
\paper Hilbert compacts, compact ellipsoids, and compact extrema
\inbook Proceedings of the Crimean autumn mathematical school-symposium
\serial CMFD
\yr 2008
\vol 29
\pages 165--175
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd128}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2472268}
\transl
\jour Journal of Mathematical Sciences
\yr 2010
\vol 164
\issue 4
\pages 637--647
\crossref{https://doi.org/10.1007/s10958-010-9766-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949279404}
Linking options:
https://www.mathnet.ru/eng/cmfd128
https://www.mathnet.ru/eng/cmfd/v29/p165
This publication is cited in the following 7 articles:
Stonyakin F.S., “Applications of Subdifferential Calculus to Bochner Integral Theory”, 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov) (Cnsa), ed. Polyakova L., IEEE, 2017, 320–323
Fedor S. Stonyakin, 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017, 1
F. S. Stonyakin, “Sequential analogues of the Lyapunov and Krein–Milman theorems in Fréchet spaces”, Journal of Mathematical Sciences, 225:2 (2017), 322–344
F. S. Stonyakin, “Anti-compacts and their applications to analogs of Lyapunov and Lebesgue theorems in Frechét spaces”, Journal of Mathematical Sciences, 218:4 (2016), 526–548
I. V. Orlov, Z. I. Khalilova, “Compact subdifferentials in Banach spaces and their applications to variational functionals”, Journal of Mathematical Sciences, 211:4 (2015), 542–578
I. V. Orlov, “Banach–Zaretsky theorem for compactly absolutely continuous mappings”, Journal of Mathematical Sciences, 180:6 (2012), 710–730
Orlov I.V., “Compact Extrema: A General Theory and Its Applications to Variational Functionals”, Modern Analysis and Applications: Mark Krein Centenary Conference, Operator Theory Advances and Applications, 190, 2009, 397–417
Citation in format AMSBIB
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