Second-order approximation of free-discontinuity problems with linear growth

Abstract

with g : [0,+∞) → [0,+∞) increasing and bounded. The approximating functionals are of AmbrosioTortorelli type and depend on the Hessian or on the Laplacian of the edge variable v which thus belongs to W (Ω). When the space dimension is equal to two and three v is then continuous and this improved regularity leads to a sequence of approximating functionals which are ready to be used for numerical simulations.