Inverse extremal problem for variational functionals


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Authors

  • Igor Orlov

Keywords:

variational functional, integrand, local extremum, non-local extremum, compact extremum, Sobolev space, dominating mixed smoothness, Legendre-Jacobi condition, compact derivative

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 C1[a; b]) or a compact extremum (in case of the Sobolev space W1,2[a; b] = H1[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.

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Published

2024-05-21

How to Cite

Orlov, I. (2024). Inverse extremal problem for variational functionals. Eurasian Mathematical Journal, 1(4). Retrieved from https://emj.enu.kz/index.php/main/article/view/61

Issue

Vol. 1 No. 4 (2010)

Section

Articles