Question: Does the quadratic functional have a minimum value when u(x) is subject to the homogeneous Neumann boundary value conditions u'(0) = u'(1) = 0? If

Does the quadratic functional

have a minimum value when u(x) is subject to the homogeneous Neumann boundary value conditions u'(0) = u'(1) = 0? If so, find all functions that minimize p[u]. Hint: What are the solutions to the associated boundary value problem?

Plu] = [* - (x - ]dx

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