Question: Compute the adjoint of the derivative operator v = D[u] = u' under the weighted inner products (11.96) on, respectively, the displacement and strain spaces.

Compute the adjoint of the derivative operator v = D[u] = u' under the weighted inner products (11.96) on, respectively, the displacement and strain spaces. Verify that all four types of boundary' conditions are allowed. Choose one set of boundary conditions and write out the self-adjoint boundary value problem D*°D[w] = f. Remark: In physics, the weight function p(x) can be identified with the density of the bar.

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