Global minimizers of the two-phase Bernoulli problem with the p-Laplace operator

In this talk, we explore the classification of Lipschitz global solutions for the two-phase p-Laplace Bernoulli problem. Our focus is on cases where the set of interior two-phase points is non-empty. We establish that, in a suitable neighborhood of certain two-phase points (referred to as regular two-phase points) the expected $C^{1,η}$ regularity holds.