Title: Regularity In Diffusion Models With Gradient Activation

Speaker:  Aelson Sobral

Abstract:  We establish sharp regularity estimates for solutions of highly degenerate fully nonlinear elliptic equations. These are free boundary models in which a nonlinear diffusion process drives the system only in the region where the gradient surpasses a given threshold. Our main result concerns the existence of a universal modulus of continuity for the gradient, up to the free boundary. We elucidate practical applications of these methods, showcasing their relevance and integration with other research trends. This is a joint work with Damiao Araujo (UFPB-Brazil) and Eduardo Teixeira (UCF-USA).