Could someone explain why can we have $\frac{\partial}{\partial c_k}E(w)=0?$
Why the author can derive respect to constants $c_k$?
Also I don't understand the rest of the solution, it's supposed to use green first identity: $$\int\int_A v\nabla u\cdot \overrightarrow n dA=\int\int\int_V\nabla v\nabla udV+\int\int\int_Vv\nabla^2u dV$$ but I don't know how.
please help