ON THE MINIMUM OF CERTAIN FUNCTIONAL

Author:

Gintaras~PURIU\v{S}KIS

2010 Mathematics Subject Classification:

49K35.

Keywords:

functional, infimum, non-fixed termination time, optimal control problem, truncated function.

Abstract:

We consider the infimum \inf \max_{j=0,1,2} \|f^{(j)}\|_{L^{\infty}(0,T_0)}, where the infimum is taken over every function f which runs through the set KC^2(0,T_0) consisting of all functions f : [0,T_0] \to {\mathbb{R}} satisfying the boundary conditions f^{(j)}(0)=a_j, f^{(j)}(T_0)=0 for j=0,1, whose derivatives f^{(j)} are continuous for j=0,1 and the second derivative f^{(2)} may have a finite number of discontinuities in the interval (0,T_0), and find this infimum explicitly for all choices of boundary conditions. We give one application of this infimum for the evaluation of truncated functions.

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Puri-2012

Vol. 7 (15), 2011