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ON THE MINIMUM OF CERTAIN FUNCTIONAL
2012
'iauliai Math. Semin
unpublished
We consider the inmum inf max j=0,1,2 ∥f (j) ∥ L ∞ (0,T0) , where the inmum is taken over every function f which runs through the set KC 2 (0, T 0) consisting of all functions f : [0, T 0 ] → 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 nite number of discontinuities in the interval (0, T 0), and nd this inmum explicitly for all choices of boundary conditions.
fatcat:oz7kplilfrhttgawyxuvh42bci