Speaker
Edgard Pimentel
(CMUC, University of Coimbra)
Description
Fully nonlinear free transmission problems have been examined from a number of perspectives. These include the existence of solutions, regularity estimates and numerical methods. However, the uniqueness of solutions remains fairly open. We resort to a relaxed notion of viscosity solutions and relate it with the usual definition. We also impose conditions on the operators driving the free transmission problem that ensure properness and, ultimately ensure the uniqueness of relaxed solutions. We conclude by discussing some consequences of our analysis to the regularity theory of relaxed solutions.
Author
Edgard Pimentel
(CMUC, University of Coimbra)