Title: Recent advances in fully nonlinear degenerate free boundary problems
Abstract: In this presentation, we discuss some developments in free transmission problems, starting with degenerate models where we establish the existence and local differentiability of solutions under minimal conditions. We then explore boundary regularity, deriving estimates for uniformly elliptic, fully nonlinear equations in free boundary settings. This work is in collaboration with Edgard Pimentel and David Jesus.
