Data: 22/06/2017 (quinta-feira)
Hora: 12:00-13:00
Local: C116

Palestrante: Professor Edgard Pimentel (PUC-Rio).

Titulo: Regularity theory for fully nonlinear PDEs

Resumo: The regularity theory for fully nonlinear PDEs was inaugurated in the turn of 70s to the 80s, with the works of Krylov and Safonov. In the span of a decade, a number of important advances took place in the field; e.g., Evans-Krylov theory and Caffarelli's estimates in Sobolev spaces. In face of those breakthroughs, the profession conjectured the possibility of a general regularity for that class of problems. Such a conjectured was set in the negative only recently; in a series of papers, Nadirashvili and Vladut produced a number of counterexamples unveiling the subtleties of this theory. In this talk, we examine $W^{2,p}$-regularity of the solutions for elliptic and parabolic fully nonlinear equations. We make use of a geometric-tangential approach, which allows us to work under asymptotic assumptions of the operator governing the problem. We also put forward a number of novelties and applications, consequential to our results.