Global comparison of finite-dimensional reduction schemes in smooth variational problems

Autor:	Yu. I. Sapronov, S. L. Tsarev
Rok vydání:	2000
Předmět:	Mechanical system Reduction (complexity) Corollary Dimensional reduction General Mathematics Mathematical analysis Banach space Key (cryptography) Applied mathematics Boundary value problem Equivalence (measure theory) Mathematics
Zdroj:	Mathematical Notes. 67:631-638
ISSN:	1573-8876 0001-4346
DOI:	10.1007/bf02676336
Popis:	A new criterion for global smooth equivalence of a pair of key functions corresponding to a smooth functional in the calculus of variations for a given pair of finite-dimensional reduction schemes is established. The statement is presented in abstract form (we consider a functional on a Banach space with a Fredholm gradient). The main condition is the possibility to deform the reduction schemes into each other preserving the coercivity of the key functions. As a corollary, we obtain the theorem concerning global smooth equivalence of the key functions calculated by the Lyapunov-Schmidt and Morse-Bott reduction schemes in the two-point boundary value problem for a natural mechanical system of sufficiently general form.
Databáze:	OpenAIRE
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