Question: Which of the following quadratic functionals possess a unique minimizer among all functions satisfying the indicated boundary conditions? Find the minimizer if it exists. a.

Which of the following quadratic functionals possess a unique minimizer among all functions satisfying the indicated boundary conditions? Find the minimizer if it exists.
a.

a( 1 ) = u(2)-0 x(1')"-u cos x | dr, u(-r) = u() = 0 (u cosx -u sin dx. u(-1) = 0.1'(1)=0 -2 11(-2) = 0, u(2) = 0

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