Massimo Gobbino

Finite Difference Approximation of the Mumford-Shah Functional

We study the pointwise convergence and the Γ of a family of nonlocal functionals defined in \input amstex \loadmsbm

Entire Solutions of the One-Dimensional Perona-Malik Equation

L^1_{\roman {loc}}(\Bbb R^n)

Finite-difference approximation of free-discontinuity problems

to a local functional that depends on the gradient of u and on the set of discontinuity points of u. We apply this result to approximate a minimum problem introduced by Mumford and Shah to study edge detection in computer vision theory.

An Example of Global Classical Solution for the Perona-Malik Equation

We prove that every function u:ℝ2 → ℝ of class C 1, satisfying the Perona-Malik equation for every (x, t) ∈ ℝ2, is a stationary affine solution, i.e., of the form u(x, t) = ax + b, where a and b are suitable real constants.

Topological properties of attractors for dynamical systems

We approximate functionals depending on the gradient of

Approximation problems for curvature varifolds

u

Optimal decay estimates for the general solution to a class of semi-linear dissipative hyperbolic equations,

and on the behaviour of

Stability of simple modes of the Kirchhoff equation

u

Higher order Glaeser inequalities and optimal regularity of roots of real functions

near the discontinuity points, by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence,

Kirchhoff equations from quasi-analytic to spectral-gap data

\Gamma