This paper is the first part of an ongoing project aimed at providing a local minimality criterion, based on a second variation approach, for the triple point configurations of the Mumford-Shah functional.

We prove an ε-regularity theorem at the endpoint of connected arcs for 2-dimensional Mumford-Shah minimizers. In particular we show that, if in a given ball Br(x) the jump set of a given MumfordShah minimizer is sufficiently close, in the Hausdorff distance, to a radius of Br(x), then in a smaller ball the jump set is a connected arc which terminates at some interior point y0 and it is C 1,α up...

We prove higher integrability for the gradient of local minimizers of the Mumford-Shah energy functional, providing a positive answer to a conjecture of De Giorgi [5].

In this paper, we present a task scheduling heuristic, based on a parallel genetic algorithm (PGA). The algorithm schedules parallel programs, represented as directed acyclic graphs (DAGs), onto multi-processor systems with dynamic interconnection networks (DIN). It combines PGA with list scheduling approach and takes into account inter-processor communication cost, link contention in the DIN a...