Let u (x) be the equilibrium solution to the Dirich let boundary value problem for a bar k u f, u,() u () 0 Prove that if f(x) 0 then the total energy at equilibrium is strictly negative p u 0

Question: Let u.(x) be the equilibrium solution to the Dirich- let boundary value problem for a bar: k[u.] = f, u,() = u.() = 0. Prove

Let u.(x) be the equilibrium solution to the Dirich- let boundary value problem for a bar: k[u.] = f, u,(ℓ) = u.(ℓ) = 0. Prove that if f(x) = 0. then the total energy at equilibrium is strictly negative: p[u.] < 0.

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