Abstract: We consider a discontinuous, fully nonlinear elliptic operator, perhaps degenerate, whose discontinuities depend on the solutions. Such dependence frames the model in the context of free boundary problems. We discuss the optimal regularity of solutions and prove the existence of viscosity solutions to this problem. We plan to detail conditions under which strong solutions exist in the uniformly elliptic setting. We close the talk with comments on further directions of research and related problems we have grown fond of recently.
This will be a hybrid seminar. All are very welcome to join either online or in person. Venue: Luigi Stasi Seminar Room (ICTP Leonardo Da Vinci Building), for those wishing to attend in person.