Title: Variations of the sharp interfaces in multiphase problems – Part V

Abstract: We will conitnue with the discussion on the regularity of a minimal surface with prescribed mean curvature and obstacle. The problem leads to a variational inequality. Then we will use a result by Breiz and Kinderlehrer to show that the minimizing surface enjoys enough regularity for taking variations. Finally, I will finish this series of talk by a discussion on the challenges of showing the regularity of the minimizers of the total solvation energy.