This article is cited in 5 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.

UDC: 517.98

MSC: Primary 49J27, 46G12; Secondary 46B25, 28C20

Received: 23.02.1998 and 20.09.1999

DOI: 10.4213/sm518

 English version: Sbornik: Mathematics, 2000, 191:10, 1527–1540

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