We consider the regularization of linear inverse problems by means of the minimization of a functional formed by a term of discrepancy to data and a Mumford-Shah functional term. The discrepancy term penalizes the L 2 distance between a datum and a version of the unknown function which is filtered by means of a non-invertible linear operator.

In the fracture model presented in this paper, the basic assumption is that the energy is the sum of two terms, one elastic and one cohesive, depending on the elastic and inelastic part of the deformation, respectively. Two variants are examined: a local model, and a nonlocal model obtained by adding a gradient term to the cohesive energy.

We extend the analysis of Chiba et al. [Phys. Rev. D 75, 124014 (2007)] of Solar System constraints on f(R) gravity to a class of nonminimally coupled (NMC) theories of gravity. These generalize f(R) theories by replacing the action functional of general relativity with a more general form involving two functions f1(R) and f2(R) of the Ricci scalar curvature R. While the function f1(R) is a nonlinear term in the action, analogous to f(R) gravity, the function f2(R) yields a NMC between the matter Lagrangian density Lm and the scalar curvature.