"Nonnegativity Criterion for a Degenerate Quadratic Form
with Two-Dimensional Control"
Abstract
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.
PDF Text
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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