A two-phase free boundary problem for an operator with nonstandard growth

. We will present recent results on a two-phase free boundary problem for an operator with non-standard growth. In fact, we consider viscosity solutions to a free boundary problem for a nonlinear elliptic PDE with non-zero right hand side. We obtain regularity results for solutions and their free boundaries. The study of PDE’s of the type considered is motivated by their application in the modelling of different phenomena, such as non-Newtonian fluids, non-linear elasticity and image reconstruction. The nonlinear degenerate/singular nature of these equations leads to challenging difficulties that will be discussed in this talk. The fact that our results hold for merely viscosity solutions allows a wide applicability