A two-phase free boundary problem involving exponential operator - Pontes, Pedro Fellype; Yang, Minbo (Topological Methods in Nonlinear Analysis, 2025)
In this paper we are interested in the study of a two-phase problem equipped with the Φ-Laplacian operator Δ_Φ u div (φ(| abla u|) abla u| abla u|), % where Φ(s)=e^s^2-1 and φ=Φ’. We obtain the existence, boundedness, and Log-Lipschitz regularity of the minimizers of the energy functional associated to the two-phase problem. Furthermore, we also prove that the free boundaries of these minimizers have locally finite perimeter and Hausdorff dimension at most (N-1).