Approximation of the Helfrich's functional via Diffuse Interfaces

We give a rigorous proof of the approximability of the so-called Helfrich's functional via diffuse interfaces, under a constraint on the ratio between the bending rigidity and the Gauss-rigidity

Quasi-potentials of the entropy functionals for scalar conservation laws

We investigate the quasi-potential problem for the entropy cost functionals of non-entropic solutions to scalar conservation laws with smooth fluxes. We prove that the quasi-potentials coincide with the integral of a suitable Einstein entropy.Comment: 26 pages, 4 figure

Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone

By using a suitable triple cover we show how to possibly model the construction of a minimal surface with positive genus spanning all six edges of a tetrahedron, working in the space of BV functions and interpreting the film as the boundary of a Caccioppoli set in the covering space. After a question raised by R. Hardt in the late 1980's, it seems common opinion that an area-minimizing surface of this sort does not exist for a regular tetrahedron, although a proof of this fact is still missing. In this paper we show that there exists a surface of positive genus spanning the boundary of an elongated tetrahedron and having area strictly less than the area of the conic surface.Comment: Expanding on the previous version with additional lower bounds, new images, corrections and improvements. Comparison with Reifenberg approac

The Γ\Gamma-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension

In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and $\Gamma$-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the space of special functions of bounded variation with vanishing diffuse gradient part. This provides a direction of investigation to derive approximation for functionals with discontinuities penalized with a "cohesive" energy, that is, whose cost depends on the actual opening of the discontinuity

Eventual regularity for the parabolic minimal surface equation

We show that the parabolic minimal surface equation has an eventual regularization effect, that is, the solution becomes smooth after a (strictly positive) finite time.Comment: 17 page

Convergence of the one-dimensional Cahn-Hilliard equation

We consider the Cahn-Hilliard equation in one space dimension with scaling a small parameter \epsilon and a non-convex potential W. In the limit \espilon \to 0, under the assumption that the initial data are energetically well-prepared, we show the convergence to a Stefan problem. The proof is based on variational methods and exploits the gradient flow structure of the Cahn-Hilliard equation.Comment: 23 page

Political Persistence, Connections and Economic Growth

Using data on a panel of 56 democratic countries in the period 1975-2004, we find evidence of a negative association between political stability and economic growth which is stronger and empirically more robust in countries with high bureaucratic costs. Motivated by these results, which contrast with previous contributions, we develop a model of growth with quality improvements where political connections with long-term politicians can be exploited by low-quality producers to defend their monopoly position and prevent innovation and entry of high-quality competitors. This requires that the incumbent politician remains in office and that the red-tape cost advantage granted by political connections is large relative to the quality upgrade related to innovation. Consistently with our empirical findings, the model delivers a negative association between the probability that the incumbent politician remains in office and average economic growth in the presence of high bureaucratic costs.political persistence, growth, innovation

Persistence of Politicians and Firms' Innovation

We empirically investigate whether the persistence of politicians in political institutions affects the innovation activity of firms. We use 12,000 firm-level observations from three waves of the Italian Observatory over Small and Medium Enterprises, and introduce a measure of political persistence defined as the average length of individual political careers in political institutions of Italian municipalities. Standard OLS shows no raw correlation between political persistence and firms’ innovation activity. However, once the causal effect is isolated by means of instrumental variables, using death of politicians as an exogenous source of variation of political persistence, we find a robust negative relation between political persistence and the probability of process innovation. This finding is consistent with the view that political stability may hinder firms’ incentive to innovate to maintain their competitiveness, as long as they can extract rents from long-term connections with politicians.innovation, politicians, tenure, instrumental variable