"Nonnegativity Criterion for a Degenerate Quadratic Form with Two-Dimensional Control"
We consider an integral quadratic form of the classical calculus of variations with two-dimensional state and control
and with the Legendre coefficient degenerate at a single point. We give a criterion of its nonnegativity in the form
of sharp inequality on its coefficients. This inequality can be, in a sense, considered as a two-dimensional
generalization of the well-known Hardy inequality on a function and its derivative.
Russian original: Критерий неотрицательности вырожденной квадратичной формы с двумерным управлением --
Итоги науки и техники. Современная мат-ка и ее приложения, М., 2002, т. 110, с. 49—75.
Talk at the Conference "Extremal problems in complex and real analysis"
Moscow, People Friendship University, May 2007.
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