Non-local Notions of Convexity

Nestor Guillen
University of California, Los Angeles (UCLA)
Department of Mathematics

Convexity has played an important role in fully nonlinear equations, for instance in obtaining pointwise bounds for viscosity solutions (in the ABP), or in understanding the regularity of the free boundary in the obstacle problem. In this talk I will describe the shortcomings of convexity when dealing with non-local problems and will discuss alternatives as well as their applications.

Back to Nonlocal PDEs, Variational Problems and their Applications