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Mat. Sb., 2000, Volume 191, Number 10, Pages 105–118 (Mi msb518)  

This article is cited in 3 scientific papers (total in 3 papers)

Variational calculus on Banach spaces

A. V. Uglanov

P. G. Demidov Yaroslavl State University

Abstract: The problem of variational calculus is considered in a (variable) subdomain of a Banach space. Analogues of the basic principles of the finite-dimensional theory are derived: the main formula for variations of a functional, necessary conditions of an extremum, Noether's theorem. All the results obtained are dimension-invariant and become the classical ones in the finite-dimensional setting. The main tool of the analysis is the theory of surface integration in Banach spaces.

DOI: https://doi.org/10.4213/sm518

Full text: PDF file (288 kB)
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English version:
Sbornik: Mathematics, 2000, 191:10, 1527–1540

Bibliographic databases:

UDC: 517.98
MSC: Primary 49J27, 46G12; Secondary 46B25, 28C20
Received: 23.02.1998 and 20.09.1999

Citation: A. V. Uglanov, “Variational calculus on Banach spaces”, Mat. Sb., 191:10 (2000), 105–118; Sb. Math., 191:10 (2000), 1527–1540

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Uglanov, AV, “Absolutely summing mappings of locally convex spaces in measure theory”, Doklady Mathematics, 64:2 (2001), 201  mathscinet  zmath  isi  elib
    2. Uglanov A.V., “On measures in locally convex spaces”, High Dimensional Probability III, Progress in Probability, 55, 2003, 43–54  mathscinet  zmath  isi
    3. 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  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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