Risultati di approssimazione per funzionali a discontinuità libera a crescita lineare
Γ-limits of convolution functionals
We compute the -limit of a sequence of non-local integral functionals depending on a regularization of the gradient term by means of a convolution kernel. In particular, as -limit, we obtain free discontinuity functionals with linear growth and with anisotropic surface energy density.
Non-local approximation of free-discontinuity problems with linear growth
We approximate, in the sense of -convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case.
Continuous limits of discrete perimeters
We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula. These functionals, based on interactions, arise in discrete optimization and are known as a large class of problems which can be solved in polynomial time. In particular, some of them can be solved very efficiently by maximal flow algorithms and are quite popular in the image processing community. We study the limit in the continuum of these functionals, show that they always converge to some...
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