= Ordinary-derivative Robin data in a weighted energy form
{title2=$a(u,v)=\int_b^cp(x)u'v'+p(c)\kappa u(c)v(c)$}
For $-(pu')'=f$, $u(b)=0$ and $u'(c)+\kappa u(c)=0$, <integration by parts> gives the displayed endpoint coefficient. Ordinary derivative data and conormal data $p(c)u'(c)+\kappa u(c)=0$ are different boundary conditions. If $p$ is bounded above and below by positive constants and $\kappa\geq0$, the <Poincaré inequality> on functions vanishing at $b$ proves continuity and coercivity. The symmetric form defines an <energy norm>, and <Galerkin orthogonality> gives exact best approximation in that norm.
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