For $\Omega\subset \mathbb{R}^2$ a smooth and bounded domain, we derive sharp universal energy estimate for non-negative solutions of free boundary problems on $\Omega$ arising in plasma physics. As consequence, are able to deduce new estimates this class problems. We first come up with positivity threshold which guarantees that there is no inside or either, equivalently, necessary condition th...

Abstract We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family minimizers to an Alt–Caffarelli–Friedman-type functional whose boundaries contain strict interior domain. also give example showing that almost-minimizers same can have very little structure. This last stands contrast with recent results De Philippis, Spolaor...

The inverse problem of reconstructing the time-dependent thermal conductivity and free boundary coefficients along with temperature in a two-dimensional parabolic equation initial conditions additional measurements is, for first time, numerically investigated. This appears extensively modelling various phenomena engineering physics. For instance, steel annealing, vacuum-arc welding, fusion cont...