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Inverse extremal problem for variational functionals

I. V. Orlov

Faculty of Mathematics and Informatics, Taurida National V. Vernadsky University, Simferopol, Ukraine

Abstract: We investigate an inverse extremal problem for the variational functionals: to describe, under certain conditions, all types of variational functionals having a local extremum (in case of the space $C^1[a;b]$) or a compact extremum (in case of the Sobolev space $W^{1,2}[a;b]=H^1[a;b]$) at a given point of the corresponding function space. The non-locality conditions for a compact extrema of variational functionals are described as well.

Keywords and phrases: variational functional, integrand, local extremum, non-local extremum, compact extremum, Sobolev space, Legendre–Jacobi condition, compact derivative, dominating mixed smoothness.

MSC: 49J05, 49L99

Received: 01.11.2010

Language: English

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