Graph-area Euler-Lagrange equation
= Graph-area Euler-Lagrange equation
{title2=$u-g-\alpha\operatorname{div}\frac{\nabla u}{\sqrt{1+|\nabla u|^2}}=0$}
For an assumed $W^{1,1}$ <minimizer> of $\alpha A(u)+\tfrac12\|u-g\|_2^2$, compactly supported variations give $u-g-\alpha\operatorname{div}(\nabla u/\sqrt{1+|\nabla u|^2})=0$ in distributions. If the regularizer is instead the <total variation seminorm>, a bounded calibration field replaces the quotient and handles zero <gradients>.