De Giorgi's approach to hyperbolic Cauchy problems: the case of nonhomogeneous equations

In this paper we discuss an extension of some results obtained by E. Serra and P. Tilli, in [Serra&Tilli '12, Serra&Tilli '16], concerning an original conjecture by E. De Giorgi ([De Giorgi '96, De Giorgi '06]) on a purely minimization approach to the Cauchy problem for the defocusing nonlinear wave equation. Precisely, we show how to extend the techniques developed by Serra and Tilli for homogeneous hyperbolic nonlinear PDEs to the nonhomogeneous case, thus proving that the idea of De Giorgi yields in fact an effective approach to investigate general hyperbolic equations.Comment: 24 page

Market regulation, labor policies and the wage-productivity gap

This paper proposes an empirical analysis about the influence of some institutional factors (taxation, active and passive labor market policies, labor and goods market regulation and unions’ participation) on the component of the wage growth not explained by the productivity growth (WP gap, thereafter). We consider a 14 OECD countries Panel Data over the period 1983-2003, using four different estimations: fixed effects vector decomposition (FEVD), fixed effects (FE), random effects (RE) and feasible general least square (FGLS). Results for all estimations show that the WP gap is affected by tax wedge, active labor market policies, employment protection for temporary workers and union density, while product market regulation and passive labor market policies do not play a significant role

Spectral partitions for Sturm-Liouville problems

We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm-Liouville problems. Via \Gamma-convergence theory, we study the asymptotic distribution of the minimizers as the number of intervals of the partition tends to infinity. Then we discuss several examples that fit in our framework, such as the sum of (positive and negative) powers of the eigenvalues and an approximation of the trace of the heat Sturm-Liouville operator

Optimal partitioning of an interval and applications to Sturm-Liouville eigenvalues

We study the optimal partitioning of a (possibly unbounded) interval of the real line into $n$ subintervals in order to minimize the maximum of certain set-functions, under rather general assumptions such as continuity, monotonicity, and a Radon-Nikodym property. We prove existence and uniqueness of a solution to this minimax partition problem, showing that the values of the set-functions on the intervals of any optimal partition must coincide. We also investigate the asymptotic distribution of the optimal partitions as $n$ tends to infinity. Several examples of set-functions fit in this framework, including measures, weighted distances and eigenvalues. We recover, in particular, some classical results of Sturm-Liouville theory: the asymptotic distribution of the zeros of the eigenfunctions, the asymptotics of the eigenvalues, and the celebrated Weyl law on the asymptotics of the counting function

Do labor market conditions affect the strictness of employment protection legislation?

We provide a theoretical microfoundation for the negative relationship between firing costs and labor market tightness and its effects on labor market performance. The optimal level of firing costs is chosen by the employed worker i.e. the insider by maximizing her human capital. Performing a comparative statics exercise, we analyze the effects of labor market tightness on the optimal choice of firing costs. The results are clear cut and allow to obtain a decreasing firing costs function in the labor market tightness. Moreover, we show that this negative relationship can give rise to a labor market configuration characterized by multiple equilibria: prolonged average duration of unemployment will produce a labor market with low flows and high strictness of employment protection, and vice versa.Matching Models