Problems with free discontinuities (Q1315156)

Some results and conjectures are presented about free discontinuity problems, which are related both to the theory of elliptic equations and of minimal surfaces. These problems appear when modeling phenomena in which both volume forces and surface tensions are present (fractures, inmiscible fluids, droplets of liquid crystals) and in the segmentation problem in computer vision theory. Many of the conjectures proposed in the paper are still unsettled and they are very interesting and difficult problems to deal with.