Fully nonlinear free transmission problems: analytical and computational findings

Speaker's Name: Edgard Pimentel
Speaker's Affiliation: University of Coimbra, Coimbra, Portugal
Speaker's Research Theme(s): Applied Mathematics
Abstract:
We discuss a class of fully nonlinear free transmission problems arising in both uniformly elliptic and degenerate regimes. These models describe situations in which the governing operator changes across an interface that is not known a priori and must be determined as part of the solution. We first present analytical results concerning the existence and regularity of solutions. We then review recent developments in the numerical approximation of these free boundary problems, with particular attention to schemes designed for fully nonlinear operators. We conclude by outlining several open problems and directions for future research, addressing both analytical and computational aspects of these models.

Venue: UP-Maths A17