Edge-free Mumford–Shah limit
= Edge-free Mumford–Shah limit
{title2=$u-\alpha\Delta u=g$}
As the jump-length weight tends to infinity with the <gradient> weight fixed, the limiting problem minimizes $\|u-g\|_2^2+\alpha\|\nabla u\|_2^2$ on $H^1$. It has a unique <minimizer> by the <Lax-Milgram theorem> and strict convexity. Without prescribed boundary values, its weak equation is $u-\alpha\Delta u=g$ with natural <Neumann boundary conditions>.