Un modello variazionale discreto del secondo ordine

We analyze a nonlinear discrete scheme depending on second-order finite differences. This is the two-dimensional analog of a scheme which in one dimension approximates a free-discontinuity energy proposed by Blake and Zisserman as a higher-order correction of the Mumford and Shah functional.
In two dimension we give a compactness result showing that the continuous problem approximating this difference scheme is still defined on special functions with bounded hessian, and we give an upper and a lower bound in terms of the Blake and Zisserman energy.